diff --git "a/data/PanMechanics_2024.tsv" "b/data/PanMechanics_2024.tsv"
new file mode 100644--- /dev/null
+++ "b/data/PanMechanics_2024.tsv"
@@ -0,0 +1,222 @@
+index	id	context	question	marking	answer	answer_type	unit	points	modality	field	source	image_question	information
+0	PanMechanics_2024_1		"由三根质量为 $M$ 、长度为 $L$ 的相同均匀杆组成一个三角形。它通过顶部的枢轴铰接在垂直平面上，如图所示。这个物理摆的小振荡周期是多少？杆子通过其质心的转动惯量为 $I_{\mathrm{CM}} = \frac{1}{12} ML^2$。
+
+[figure1]
+
+(A) $\sqrt{\frac{3L}{2g}}$ 
+(B) $2\pi \sqrt{\frac{3L}{g}}$ 
+(C) $\pi \sqrt{\frac{3L}{g}}$ 
+(D) $\pi \sqrt{\frac{3ML}{g}}$ 
+(E) $\pi \sqrt{\frac{2\sqrt{3}L}{g}}$"		"[""\\boxed{E}""]"	"[""Multiple Choice""]"	[null]	[2.0]	text+illustration 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$g = 10 m/s^2$ 及 重力常数 $G = 6.67 \times 10^{-11} N m^2/\mathrm{kg}^2$（若没有特别注明，取所有摩擦力为零）。
+1	PanMechanics_2024_2		"一辆以 $36 m/s$ 速度行驶的卡车经过一辆以 $45 m/s$ 速度朝相反方向行驶的警车。如果警笛相对于警车的频率为 $500 Hz$,那么当警车接近卡车时,卡车内的观察者听到的频率是多少？(空气中的声速为 $343 m/s$) 
+
+(A) $396 \mathrm{Hz}$ 
+(B) $636 \mathrm{Hz}$ 
+(C) $361 \mathrm{Hz}$ 
+(D) $393 \mathrm{Hz}$ 
+(E) $617 \mathrm{Hz}$"		"[""\\boxed{B}""]"	"[""Multiple Choice""]"	[null]	[2.0]	text-only	Mechanics	PanMechanics_2024		若有需要，取重力加速度 $g = 10 m/s^2$ 及 重力常数 $G = 6.67 \times 10^{-11} N m^2/\mathrm{kg}^2$（若没有特别注明，取所有摩擦力为零）。
+2	PanMechanics_2024_3		"一颗卫星绕 X 行星做圆形轨道运行，且轨道距离行星表面非常近。要估计行星 X 的密度，我们只需测量：
+
+(A) 卫星的周期 
+(B) 轨道半径 
+(C) 卫星的速度 
+(D) 行星 X 的质量 
+(E) 卫星的质量"		"[""\\boxed{A}""]"	"[""Multiple Choice""]"	[null]	[2.0]	text-only	Mechanics	PanMechanics_2024		若有需要，取重力加速度 $g = 10 m/s^2$ 及 重力常数 $G = 6.67 \times 10^{-11} N m^2/\mathrm{kg}^2$（若没有特别注明，取所有摩擦力为零）。
+3	PanMechanics_2024_4	质量为 $M$ 的三角楔子置于水平无摩擦的地面上。将质量为 $m$ 的木块放在楔子上，如图所示。木块和楔子之间没有摩擦力。系统从静止状态释放。给定 $M = 3m$ 和 $\alpha = 45^{\circ}$。	"求三角楔子加速度的大小。
+
+(A) $g/6$ 
+(B) $g/7$ 
+(C) $g/4$ 
+(D) $g$ 
+(E) 0"		"[""\\boxed{B}""]"	"[""Multiple Choice""]"	[null]	[2.0]	text+illustration figure	Mechanics	PanMechanics_2024	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	若有需要，取重力加速度 $g = 10 m/s^2$ 及 重力常数 $G = 6.67 \times 10^{-11} N m^2/\mathrm{kg}^2$（若没有特别注明，取所有摩擦力为零）。
+4	PanMechanics_2024_5	质量为 $M$ 的三角楔子置于水平无摩擦的地面上。将质量为 $m$ 的木块放在楔子上，如图所示。木块和楔子之间没有摩擦力。系统从静止状态释放。给定 $M = 3m$ 和 $\alpha = 45^{\circ}$。	"若当木块滑到地面时，楔子相对地面的速度为 $1 m/s$。求木块在楔子上离地面的初始高度（假设木块为无体积的重点）。 
+
+(A) $0.60 m$ 
+(B) $0.82 m$ 
+(C) $1.00 m$ 
+(D) $1.05 m$ 
+(E) $1.40 m$"		"[""\\boxed{E}""]"	"[""Multiple Choice""]"	[null]	[2.0]	text+illustration figure	Mechanics	PanMechanics_2024	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	若有需要，取重力加速度 $g = 10 m/s^2$ 及 重力常数 $G = 6.67 \times 10^{-11} N m^2/\mathrm{kg}^2$（若没有特别注明，取所有摩擦力为零）。
+5	PanMechanics_2024_6		"在一维运动中，力 $F = -(m/b) v^2$ 作用在质量为 $m$ 的粒子上，其中 $v$ 是粒子的速度，$b$ 是常数。在 $t = 0 s$ 时，该粒子位于 $x = 0 m$。哪一个是粒子随时间变化的可能位置？
+
+(A) $x(t) = b \ln (\frac{t}{1 \mathrm{s}})$ 
+(B) $x(t) = b \ln (\frac{t}{1 \mathrm{s}} + 1)$ 
+(C) $x(t) = b \frac{t / 1\mathrm{s}}{2 + ( t/1\mathrm{s})^2}$ 
+(D) $x(t) = \frac{b}{t/1\mathrm{s}}$ 
+(E) $x(t) = b \sin (t/1\mathrm{s})$"		"[""\\boxed{B}""]"	"[""Multiple Choice""]"	[null]	[2.0]	text-only	Mechanics	PanMechanics_2024		若有需要，取重力加速度 $g = 10 m/s^2$ 及 重力常数 $G = 6.67 \times 10^{-11} N m^2/\mathrm{kg}^2$（若没有特别注明，取所有摩擦力为零）。
+6	PanMechanics_2024_7	一个体重 $60 \mathrm{kg}$ 的人以 $5 m/s$ 的初始速度沿着半径为 $3 m$、质量为 $100 \mathrm{kg}$ 的固定均匀圆形平台的切线跑步，如图所示。平台本来静止，当人跳上及静止在平台上后，平台绕中心的垂直轴旋转。圆形平台通过其质心的转动惯量为 $I_{\mathrm{CM}} = \frac{1}{2} M R^2$。	"求该人跳上平台后系统的角速度。
+
+(A) 0.500 rad/s 
+(B) 0.250 rad/s 
+(C) 1.33 rad/s 
+(D) 0.909 rad/s 
+(E) 1.705 rad/s"		"[""\\boxed{D}""]"	"[""Multiple Choice""]"	[null]	[2.0]	text+illustration figure	Mechanics	PanMechanics_2024	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	若有需要，取重力加速度 $g = 10 m/s^2$ 及 重力常数 $G = 6.67 \times 10^{-11} N m^2/\mathrm{kg}^2$（若没有特别注明，取所有摩擦力为零）。
+7	PanMechanics_2024_8	一个体重 $60 \mathrm{kg}$ 的人以 $5 m/s$ 的初始速度沿着半径为 $3 m$、质量为 $100 \mathrm{kg}$ 的固定均匀圆形平台的切线跑步，如图所示。平台本来静止，当人跳上及静止在平台上后，平台绕中心的垂直轴旋转。圆形平台通过其质心的转动惯量为 $I_{\mathrm{CM}} = \frac{1}{2} M R^2$。	"找出总机械能的损失。
+
+(A) $150 J$ 
+(B) $341 J$ 
+(C) $257 J$ 
+(D) $457 J$ 
+(E) $0 J$"		"[""\\boxed{B}""]"	"[""Multiple Choice""]"	[null]	[2.0]	text+illustration figure	Mechanics	PanMechanics_2024	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	若有需要，取重力加速度 $g = 10 m/s^2$ 及 重力常数 $G = 6.67 \times 10^{-11} N m^2/\mathrm{kg}^2$（若没有特别注明，取所有摩擦力为零）。
+8	PanMechanics_2024_9	两个 $1.0 \mathrm{kg}$ 的粒子以 $(40.0 m/s) \hat{l}$ 和 $(-20.0 m/s) \hat{l}$ 的速度沿直线相互移动并發生碰撞。碰撞后，其中一个粒子以 $30.0 m/s$ 的速度离开。在碰撞过程中，两颗粒子共损失了 $100 \mathrm{J}$ 的能量。	"求碰撞后另一个粒子的速度。
+
+(A) $33.2 m/s$ 
+(B) $36.1 m/s$ 
+(C) $17.3 m/s$ 
+(D) $26.8 m/s$ 
+(E) $30.0 m/s$"		"[""\\boxed{E}""]"	"[""Multiple Choice""]"	[null]	[2.0]	text-only	Mechanics	PanMechanics_2024		若有需要，取重力加速度 $g = 10 m/s^2$ 及 重力常数 $G = 6.67 \times 10^{-11} N m^2/\mathrm{kg}^2$（若没有特别注明，取所有摩擦力为零）。
+9	PanMechanics_2024_10	两个 $1.0 \mathrm{kg}$ 的粒子以 $(40.0 m/s) \hat{l}$ 和 $(-20.0 m/s) \hat{l}$ 的速度沿直线相互移动并發生碰撞。碰撞后，其中一个粒子以 $30.0 m/s$ 的速度离开。在���撞过程中，两颗粒子共损失了 $100 \mathrm{J}$ 的能量。	"求碰撞后粒子速度之间的夹角。
+
+(A) $141^{\circ}$ 
+(B) $105^{\circ}$ 
+(C) $70.5^{\circ}$ 
+(D) $96.4^{\circ}$ 
+(E) $48.2^{\circ}$"		"[""\\boxed{A}""]"	"[""Multiple Choice""]"	[null]	[2.0]	text-only	Mechanics	PanMechanics_2024		若有需要，取重力加速度 $g = 10 m/s^2$ 及 重力常数 $G = 6.67 \times 10^{-11} N m^2/\mathrm{kg}^2$（若没有特别注明，取所有摩擦力为零）。
+10	PanMechanics_2024_11		"如图所示，粒子在 $x = a$ 点从静止状态释放，并根据图中所示的势能函数 $U(x)$ 沿 $x$ 轴移动。图中 $U(a) = U(e)$。粒子其后的运动为：
+
+(A) 移动到 $x = e$ 左侧的点，停止并保持静止。
+(B) 在 $x = a$ 及 $x = e$ 之间来回移动。
+(C) 以不同的速度移动到无穷大 $(x \rightarrow \infty)$。
+(D) 移动到 $x = b$，并保持静止状态。
+(E) 移动到 $x = e$，然后移动到 $x = d$，并保持静止状态。"		"[""\\boxed{B}""]"	"[""Multiple Choice""]"	[null]	[2.0]	text+data figure	Mechanics	PanMechanics_2024	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	若有需要，取重力加速度 $g = 10 m/s^2$ 及 重力常数 $G = 6.67 \times 10^{-11} N m^2/\mathrm{kg}^2$（若没有特别注明，取所有摩擦力为零）。
+11	PanMechanics_2024_12		"逃离木星引力的最低速度为 60 公里/秒。假设木星的半径为 70,000 公里，那么 80 公斤重的宇航员在木星上的重量是多少？
+
+(A) $1029 N$ 
+(B) $1371 N$ 
+(C) $2057 N$ 
+(D) $2742 N$ 
+(E) $4114 N$"		"[""\\boxed{C}""]"	"[""Multiple Choice""]"	[null]	[2.0]	text-only	Mechanics	PanMechanics_2024		若有需要，取重力加速度 $g = 10 m/s^2$ 及 重力常数 $G = 6.67 \times 10^{-11} N m^2/\mathrm{kg}^2$（若没有特别注明，取所有摩擦力为零）。
+12	PanMechanics_2024_13		"下列哪一个人必须是非惯性观察者？将地面视为惯性系。应考虑空气摩擦力。
+I. 一个人的位置被另一个观察者描述为 $y(t) = -\frac{g}{2} t^2$。
+II. 坐在固定在地面上旋转的旋转木马边缘的人。
+III. 一个人垂直向上跳跃。而此刻，当人处于最高位置时。
+IV. 一个人垂直向上跳跃。而此刻，人还在上升的时候。
+V. 一个戴着打开的降落伞进行跳伞的人。
+
+(A) 只有 I, IV 和 V 
+(B) 只有 I 和 II 
+(C) 只有 I,II,IV 和 V 
+(D) 只有 II, III 和 IV 
+(E) I, II, III, IV 和 V"		"[""\\boxed{D}""]"	"[""Multiple Choice""]"	[null]	[2.0]	text-only	Mechanics	PanMechanics_2024		若有需要，取重力加速度 $g = 10 m/s^2$ 及 重力常数 $G = 6.67 \times 10^{-11} N m^2/\mathrm{kg}^2$（若没有特别注明，取所有摩擦力为零）。
+13	PanMechanics_2024_14		"如图所示一个 3.0 kg 的三角体，求推动三角体的力 $F$，使在三角块上的 1.0 kg 方形块不会沿斜面移动。假设所有表面都是无摩擦的。
+
+(A) $15 N$ 
+(B) $20 N$ 
+(C) $25 N$ 
+(D) $40 N$ 
+(E) $45 N$"		"[""\\boxed{D}""]"	"[""Multiple Choice""]"	[null]	[2.0]	text+illustration figure	Mechanics	PanMechanics_2024	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	若有需要，取重力加速度 $g = 10 m/s^2$ 及 重力常数 $G = 6.67 \times 10^{-11} N m^2/\mathrm{kg}^2$（若没有特别注明，取所有摩擦力为零）。
+14	PanMechanics_2024_15		"一个边长为 $L$ 的正方体平稳地漂浮在容器内静止的水中。此时有一半的立方体位于水面以下。再将密度为水四分之一的液体添加到容器中，使立方体完全浸没在液体的表面下，而液体和水不混合，液体留在水上面。添加液体后，立方体从原來的水面上升了多少？
+
+(A) $L/6$ 
+(B) $L/3$ 
+(C) $L/2$ 
+(D) $L/4$ 
+(E) $L/5$"		"[""\\boxed{A}""]"	"[""Multiple Choice""]"	[null]	[2.0]	text-only	Mechanics	PanMechanics_2024		若有需要，取重力加速度 $g = 10 m/s^2$ 及 重力常数 $G = 6.67 \times 10^{-11} N m^2/\mathrm{kg}^2$（若没有特别注明，取所有摩擦力为零）。
+15	PanMechanics_2024_16		"一个盒子由两根具有相同线性质量密度的绳子悬挂在天花板上，如图所示。求弦 1 的基频 $f_1$ 与弦 2 的基频 $f_2$ 之比，$f_1 / f_2$。
+
+(A) $\sqrt{3 \sqrt{3}}$ 
+(B) 3 
+(C) $3 \sqrt{3}$ 
+(D) $\sqrt{6}$ 
+(E) $\sqrt{3}/4$"		"[""\\boxed{A}""]"	"[""Multiple Choice""]"	[null]	[2.0]	text+variable figure	Mechanics	PanMechanics_2024	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	若有需要，取重力加速度 $g = 10 m/s^2$ 及 重力常数 $G = 6.67 \times 10^{-11} N m^2/\mathrm{kg}^2$（若没有特别注明，取所有摩擦力为零）。
+16	PanMechanics_2024_17_1	质量为 $m$ 的质点附着在力常数为 $k$ 的弹簧上，在粗糙表面上沿 X 轴移动。以原点为弹簧自然长度时的位置。	当 $t = 0$ 时，粒子在 $x_0 \neq 0$ 及静止。假设弹簧力足够大，使得粒子在恒定的摩擦力 $f$ 下移动。在时间 $0 \leq t \leq \tau$ 内，求 $x(t)$，其中 $\tau$ 是 $t = 0$ 后粒子第一次停止的时间。用 $k$、$m$、$f$ 和 $x_0$ 表示 $x(t)$。设静摩擦系数为 0.03，动摩擦系数为 0.01，$m = 1 \mathrm{kg}$，$k = 10 \mathrm{N}/\mathrm{m}$，重力加速度 $g = 10 m/s^2$。		"[""\\boxed{$x(t) = (x_0 - \\frac{f}{k}) \\cos(\\sqrt{\\frac{k}{m}}t) + \\frac{f}{k}$}"", ""\\boxed{$x(t) = (x_0 + \\frac{f}{k}) \\cos(\\sqrt{\\frac{k}{m}}t) - \\frac{f}{k}$}""]"	"[""Expression"", ""Expression""]"	[null]	[8.0, 8.0]	text-only	Mechanics	PanMechanics_2024		若有需要，取重力加速度 $g = 10 m/s^2$ 及 重力常数 $G = 6.67 \times 10^{-11} N m^2/\mathrm{kg}^2$（若没有特别注明，取所有摩擦力为零）。
+17	PanMechanics_2024_17_2	"质量为 $m$ 的质点附着在力常数为 $k$ 的弹簧上，在粗糙表面上沿 X 轴移动。以原点为弹簧自然长度时的位置。
+(a) 当 $t = 0$ 时，粒子在 $x_0 \neq 0$ 及静止。假设弹簧力足够大，使得粒子在恒定的摩��力 $f$ 下移动。在时间 $0 \leq t \leq \tau$ 内，求 $x(t)$，其中 $\tau$ 是 $t = 0$ 后粒子第一次停止的时间。用 $k$、$m$、$f$ 和 $x_0$ 表示 $x(t)$。设静摩擦系数为 0.03，动摩擦系数为 0.01，$m = 1 \mathrm{kg}$，$k = 10 \mathrm{N}/\mathrm{m}$，重力加速度 $g = 10 m/s^2$。
+注意：（a）是前置问题，请不要写入最终答案中。"	设 $x_0 = 1 m$。使用 (a) 或其他方式，找到粒子永久停止时的最终位置。（单位用 $m$ 表示）		"[""\\boxed{-0.02}""]"	"[""Numerical Value""]"	"[""m""]"	[8.0]	text-only	Mechanics	PanMechanics_2024		若有需要，取重力加速度 $g = 10 m/s^2$ 及 重力常数 $G = 6.67 \times 10^{-11} N m^2/\mathrm{kg}^2$（若没有特别注明，取所有摩擦力为零）。
+18	PanMechanics_2024_17_3	"质量为 $m$ 的质点附着在力常数为 $k$ 的弹簧上，在粗糙表面上沿 X 轴移动。以原点为弹簧自然长度时的位置。
+(a) 当 $t = 0$ 时，粒子在 $x_0 \neq 0$ 及静止。假设弹簧力足够大，使得粒子在恒定的摩擦力 $f$ 下移动。在时间 $0 \leq t \leq \tau$ 内，求 $x(t)$，其中 $\tau$ 是 $t = 0$ 后粒子第一次停止的时间。用 $k$、$m$、$f$ 和 $x_0$ 表示 $x(t)$。设静摩擦系数为 0.03，动摩擦系数为 0.01，$m = 1 \mathrm{kg}$，$k = 10 \mathrm{N}/\mathrm{m}$，重力加速度 $g = 10 m/s^2$。
+(b) 设 $x_0 = 1 m$。使用 (a) 或其他方式，找到粒子永久停止时的最终位置。（单位用 $m$ 表示）。
+注意：(a) 和 (b) 都是前置问题，请不要写入最终答案中。"	求出粒子的总移动距离。（单位用 $m$ 表示）		"[""\\boxed{49.98}""]"	"[""Numerical Value""]"	"[""m""]"	[6.0]	text-only	Mechanics	PanMechanics_2024		若有需要，取重力加速度 $g = 10 m/s^2$ 及 重力常数 $G = 6.67 \times 10^{-11} N m^2/\mathrm{kg}^2$（若没有特别注明，取所有摩擦力为零）。
+19	PanMechanics_2024_17_4	"质量为 $m$ 的质点附着在力常数为 $k$ 的弹簧上，在粗糙表面上沿 X 轴移动。以原点为弹簧自然长度时的位置。
+(a) 当 $t = 0$ 时，粒子在 $x_0 \neq 0$ 及静止。假设弹簧力足够大，使得粒子在恒定的摩擦力 $f$ 下移动。在时间 $0 \leq t \leq \tau$ 内，求 $x(t)$，其中 $\tau$ 是 $t = 0$ 后粒子第一次停止的时间。用 $k$、$m$、$f$ 和 $x_0$ 表示 $x(t)$。设静摩擦系数为 0.03，动摩擦系数为 0.01，$m = 1 \mathrm{kg}$，$k = 10 \mathrm{N}/\mathrm{m}$，重力加速度 $g = 10 m/s^2$。
+(b) 设 $x_0 = 1 m$。使用 (a) 或其他方式，找到粒子永久停止时的最终位置。（单位用 $m$ 表示）。
+(c) 求出粒子的总移动距离。（单位用 $m$ 表示）
+注意：(a)、(b) 和 (c) 都是前置问题，请不要写入最终答案中。"	求粒子永久停止之前所经过的总时间。（单位用 $s$ 表示）		"[""\\boxed{48.68}""]"	"[""Numerical Value""]"	"[""s""]"	[3.0]	text-only	Mechanics	PanMechanics_2024		若有需要，取重力加速度 $g = 10 m/s^2$ 及 重力常数 $G = 6.67 \times 10^{-11} N m^2/\mathrm{kg}^2$（若没有特别注明，取所有摩擦力为零）。
+20	PanMechanics_2024_18_1	"总质量为 $M$ 的弹性弹簧在未拉伸时具有均匀的质量分布。其弹簧常数为 $K$，为简单起见，假设其自然长度为零。现在它从顶端悬挂起来，并在恒定重力 $g$ 下垂直悬挂并达至静止状态。
+
+[figure1]
+
+如图 1 所示，在 $t = 0 s$ 时，顶端从静止状态释放，弹簧落下。为了理解它的下落运动，我们可以将弹簧建模为一系列 $N$ 个质量为 $m_N$ 的相同质量，与 $N - 1$ 个具有弹簧常数 $k_N$ 和零自然长度的相同弹簧连接。
+
+[figure2]
+
+如图 2 所示，坐标 $x_1, x_2, \cdots x_N$ 分别是距离底部 $(x_1)$ 和顶部 $(x_N)$ 位置的质量，从天花板开始测量（向下为正）。在 $t = 0 s$ 时，$x_N = 0 m$。"	求 $k_N$ 。答案以 $K$ 表示。		"[""\\boxed{$k_N = (N-1) K$}""]"	"[""Expression""]"	[null]	[2.0]	text+variable figure	Mechanics	PanMechanics_2024	"[""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"", 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Uk8CvCPFV5a6h4z1m6srmG5t3mi2SwuHRsQRA4I4PII/Cve3RZEZHUMrDBUjII9K8o1/4ZX0Wrp/wj4i+wXL/MsrYFme5A6snoByDx06dmCqQp1OabMMRCU42idl4E1XTr3wjo9raX9rPcW+n26zRRTKzxkRqCGAORyCOa6asjw74dsfDWmLZ2almJ3TTP9+Z+7Mf6dAK165ZWu7GyvbUKKKKkYUUUUAZuuf8AIPi/6/LX/wBHx1pVm65/yD4v+vy1/wDR8daVW/gXq/0J+0Zuh/8AIPl/6/Lr/wBHyVpVm6H/AMg+X/r8uv8A0fJWlRU+NhH4UZkzA+KLJc8iyuCf++4f8K06yZf+Rvtf+vCb/wBGRVrUT2Xp+oR3YUUUVBQUUUUAV76zW/s5LZ5Z4lkGC9vK0bj6MpBFeT/ErT9J8F+G5NRk1fVp7yQ7LW3uZ0nWR/8Aa8xGO0d/wHGa9W1HUbTSdPmv76YQ20IzJIQSFGcdq+efjl4p0Txdp2lNod6br7E8pmxBIoAbZj5ioB+6e9NbiZ5Bfa1f6hcNNLNtJOdsShFH0AwBXYeAvijrHhS9SGUx3ti5wYrkZ2ehVuo/l7V5/UkEMlxcRwxKWkdgqgDJJppsLI+zNM8Q+Kr0QSt4Wg+zShWE0eoqRtP8QBUZGOa6+uF8N6H420/TdOt5tc0+KCCGOMwSWfmlVVQNuQUx0x3/ABruqljCiiigAooooAKKKKACiiigAooooAzdc/5B8X/X5a/+j460qzdc/wCQfF/1+Wv/AKPjrSq38C9X+hP2jN0P/kHy/wDX5df+j5K0qzdD/wCQfL/1+XX/AKPkrSoqfGwj8KMZ/wDkdIP+wdJ/6MStmsRv+R4j/wCwa3/oxa26dTp6BHqFFFFZlBRRRQBWv71NPspbqSKeVYxkpbxNK5+iqCTXA6/4z8O6rYzWWp6DdTQyqUYXax25x7GVlIPvXe6ldy2OnzXMFnLeSxjKwQkB356DPFcZJ4+1sOV/4QjVrYD/AJaXABT80zQB4jJ8If7Wv3fRdW0+3tHOUS8vY3ZR6Exk5rsPCnwNudLuVu5tW06S7QgxSwyO/lnswA28/jXW3Ovxak2zUI/DEBbtdQSyN+IaMD9aE8OaVfgFdf0K3U/w2NoICPoRIP5U7isbVh4R8T2s6PP48vZYlYEwrZxAMM9Mtub9a7SuH0zwBZQTRzweJ9dkKMG2pqBaM4OcEHdx+NdxSGFFFFABRRRQAUUUUAFFFFABRRRQBm65/wAg+L/r8tf/AEfHWlWbrn/IPi/6/LX/ANHx1pVb+Ber/Qn7Rm6H/wAg+X/r8uv/AEfJWlWbof8AyD5f+vy6/wDR8laVFT42EfhRidfHI9tNOP8Av7/9atusQc+OWPppo/WU/wCFbdOp09Aj1Ciiq2oy+Tpl3L9o+zbIXbz9m/y8Kfm298dcd8VmUWaKy/Dd19t8Nabdf2j/AGl5tuj/AG3yPJ8/I+/s/hz1x2rUoAKQjIxnHuKWigClPYzTAgaldRg9lSIj/wAeQ1h3ngSw1Ak3N7eOT3Cwg/pHWt4hvLmw0C8urO4062uI0zHLqTlLdDkcuRyBWhExeFGYoWKgkoflJ9vagDlrX4c+HrWdJvKupJEIZS9y45HspArrKKKACiszxDeXNhoF5dWdxp1tcRpmOXUnKW6HI5cjkCtCJi8KMxQsVBJQ/KT7e1AD6KKKACiiigAooooAKKKKAM3XP+QfF/1+Wv8A6PjrSrN1z/kHxf8AX5a/+j460qt/AvV/oT9ozdD/AOQfL/1+XX/o+StKs3Q/+QfL/wBfl1/6PkrSoqfGwj8KMVRnxtKfTTk/WRv8K2qx4wT4zuD2GnxA/wDfyT/CtinU3Xogj1CorhJZLWWOCbyZmQhJdobYxHDYPXB5xUtFZlFXTYLq2022gvrz7bdxxhZbnyhH5rActtHC59BVqiigAooqOd5EjLRLGzD/AJ6OVH54NAFDxDZ3N/oF5a2dvp1zcSJiOLUkL27nI4cDkitCJSkKKwQMFAIQfKD7e1eS+IPjrYaDqZs1s7G/2HDva37sFP4wgH8DWhpPxq0bVLcyrZSDBAKreW6sD7CR0J/AGnZiuj02iuY0nxzp2r3cdtDY6qjyHAZrJ2jH1kTcoHuTiunpDMzxDZ3N/oF5a2dvp1zcSJiOLUkL27nI4cDkitCJSkKKwQMFAIQfKD7e1PooAKKKKACiiigAooooAKKKKAM3XP8AkHxf9flr/wCj460qzdc/5B8X/X5a/wDo+OtKrfwL1f6E/aM3Q/8AkHy/9fl1/wCj5K0SMgg559DisHS9H0y8tpprnTbOeU3l1l5YFZj+/k7kVp/2Rpn2X7L/AGdafZt2/wAnyF2bvXGMZ96qpy8z16ijeyPO9N0rWz8QJbCXUr9oYMPJKbh8vCDlFJzzknGO2Wr1CsmfTbbTIHutI0OykvlwIlRUhyScHL4O0AEk4BOAcAniue8IXGneL9Pi1VfCen2thLECJJUUyNMMB1C+WMqrbl3kgkqflxzV1qqqtN6WXYmnBwTsdvRVOfSNMuvL+0adaTeWoRPMgVtqjoBkcD2oj0jTIoJYI9OtEhlx5kawKFfHTIxg1jaPc01LlFUItD0iCVJYdKsY5EOVdLdAVPqCBRLoekTyvLNpVjJI5yzvboSx9SSKLR7/ANfeGo3WtKOsWBtRqN9YfMG86ykCScdskHivCfjFp7+DtGto7fxDrV/LqDuhF7etIFVQM8Agc7h2r27WtA0PUdKjstRhjis4m3RiOUwBDz0Kkep46V5F8UfAuhnwu0+h6oDeWriVbdrlX3r3weu4deT696a5e4nc+duprR0HWrzw9rVrqlhKY7i3kDqQevsfUe1MfVtVBZJNQvB2KtM3+NaXhXTvEGt6jHp2jG9bJ3MsDsFUdycdPrQlG+/9feDbsfVvh3xzd681mD4U1q3iuFVvtboggAIzuBLbivocV2VcF4dGv/ZrPSNS8EWcOmjaskv2uOQcD77IQCzcdcZrsLfRtLtJlmttNs4ZVzh44FVh+IFJ8o9S7RWc3h/RWYs2kWBYnJJtk5/SpZ9I0y5EYuNOtJREuyMSQK2xfQZHA9qLR7/194alyio4LeG1hWG3hjhiX7qRqFUfQCpKkYUUUUAFFFFABRRRQBm65/yD4v8Ar8tf/R8daVZuuf8AIPi/6/LX/wBHx1pVb+Ber/Qn7Rm6H/yD5f8Ar8uv/R8laVZuh/8AIPl/6/Lr/wBHyVpUVPjYR+FFHVdN/tWy+yNeXVtGzDzTbMqtIndCxBIB7lcN6EVz/wDwiA0LwvrdloNzqJa4jlktLVbkRrA5LuI4SAvlqWYjOc4P3hgY66ioKOL8GaR4g0bV7231Sa9u7Q2dsqXd1emYPMqnzCqEkrksQeFGEU/MSTXaUUUAFFFFAFHVdH07XLP7HqlnFd2+4N5cq5GR3rAT4beFLMmSx0gWknXdayMh/niutooA8u1r4U6Fqd01zPpmsXE7cl/Ntzk+5LAn86fpfh/xJ4Zt/svh3ThbwE8rJHbAt/vMGya9Oop3YrHL6RJ41a7iGp2+kraZ/eFXbzMewHGa6iiikMKKKKACiiigAooooAKKKKACiiigDN1z/kHxf9flr/6PjrSrN1z/AJB8X/X5a/8Ao+OtKrfwL1f6E/aM3Q/+QfL/ANfl1/6PkrSrN0P/AJB8v/X5df8Ao+StKip8bCPwoKKKKgoKrajF52mXcX2f7TvhdfI37PMyp+Xd2z0z2zVmori3iu7WW2nXfDMhjdckZUjBGR7UAUPDdr9i8Naba/2d/ZvlW6J9i8/zvIwPub/4sdM961Kq6bp1rpGm22nWMXlWltGIoo9xbaoGAMkkn8atUAFFV729t9Os5Lu7k8uCMZd8E47dBzXOSfEjwsrbU1JZG7BVIP8A49igDS8Wf8itqH/IW/1X/MH/AOPvqP8AVf7X9M1qwf8AHvF/rPuD/Wfe6d/euXvdcg8RaTcWVnBrkYnXb9osGSOVPdWLcGtm01G4ZERtI1GPaAN0zQkn3OJDQBp0UxXY4zE4+pH+NPoAxvFll/aHhbULT+yf7W82Lb9h+0+R5/I+XzP4fXPtWrAuy3iXZ5eEA2Zzt46Z71X1bSrLXNKuNM1GHz7O4XZLHvZdwznqpBHTsatRosUaxoMKoCgegFADqKKKACiiigAooooAKKKKAM3XP+QfF/1+Wv8A6PjrSrN1z/kHxf8AX5a/+j46XXn1CPRbmXTGAu413oCu7djkjHqRnHvWiXMkvP8AyJbs2xND/wCQfL/1+XX/AKPkrSrgfh7qusarLctcSJ9hiZ2OIwC0rsXOD+JP4iu+qsRTcKjiyaUlKCaCiiisTQKKKKACiiigCrqE81tYSzW9m95KoysCMFL89MniuMm8Sa07Ms3w+uYl/wCekksUgP4Jk12t6l29nItjNDDckfJJNGZFB91BBP51wPie+8XeGdHuNX1DxBYi1gGSsEAjZz2VQyvyaAK801tdn/TNF0m3z18/SLlsfjsC/rTY9P0uVgsXijTtPJ/gtd9uw+mXB/SvFtX+M/iq9uWNnqNxbQZ+UeZ82PcqAPyAroPBvxS07UpxYeMbW6uS/CXCXDnJ9GUt+o/KnYVz2TTfD6RzRyJ441SfawOz7arq3sd2T+tdrXmOl3nw6kvoVttBnFxvAR5NLlOGzwdxUjr3zXp1IYUUUUAFFFFABRRRQAUUUUAFNcOY2EbKr4O0sMgH3GRn86dRQBz2sQ6uLKIy31iyfa7bhbN1OfOTHPmnvj/63WtS4i1Npiba8s44uyy2rOw/ESL/ACqLXP8AkHxf9flr/wCj460q1cnyp+vT0IUVdmRYaTcaZprW1nNZRStM0pYWrbPm5I2+ZnPvnoAMVat4tTWYG5vLOSLusVqyMfxMjfyrjvijqklho2/S9Ruk1uzX7bDaW0pw0aMrPJKgIJjCo6/MdpLYwW2407O/ay8JwX2gM2uJM7SSXd/ftEmAG3yl3DbUymAqLt+YEALk1Lm3e41FLY2TDrWTjUNPA7ZsX/8AjtTTxam3l/Z7u0jwoD+Zas+W7kYkGB7c/Wo9D1J9Y0Gw1KS0ktHuoEma3kOWjLAHBPf9PoOlaFLnf9JD5UU44tTEEoku7Rpjjy3W1ZVX1yvmEn8xUcUOriVDLfWLRgjcqWbqSPY+acfka0KKOZ/0g5UUJodWaZjDe2SRk/Kr2bsQPciUZ/IU94tTNvGsd3aLOM+Y7WrFW9ML5gI/M1coo5n/AEgsjHvbe5bTLpNV1aCC3ZP9fbq9q0Zz13+YcfpXz18WYrCxsbOOPxPJr6yu5kSK+3+SRjaW3NIecn06V9I6q9vHpk7XVo93AAN0CReYX5/u968s8XW/hbXdBudOXwtfWUsgzHcJYrE0bjofceopqbv/AMATifNED2Kx4uLe4kfPWOdUGPoUP86VJLRb1HSC4EQxhPPG/d/vbMfpWtqfg3WNNn2G381D914yDx7+n412XgL4Sajrc0d9eXlhawoQyRSSh3c+6KcgfUii7DQ9v8M6r41mstNNxodo1m0EeZHm2SkFR8x689zwPwrrXh1kuxS/sAueAbJyQPr5tYVloHi+CWPz/F8TwowzFHpyDI9MsSa29Q1qLTtX0rTntriR9Skkjjkj27IyiFzvywPIBxgHpzjIyc7vf9EHLoTzxamwj+z3dpGQuJPMtWfc3qMSDA9ufrT7RL1A/wBsuLeYnG3yYGjx65y7Z/SrNFLmdrDsFFFFSMKKKKACiiigAooooAzdc/5B8X/X5a/+j460q4H4h6hrOlvay2txiwkZSV8tTtlRg45I74Bx/smus0D+0G0S2k1STfeSLvf5Au3PIXAA5Axn3zW86TjSjO+5lGd5uNjSrJ8QaEviCyjtX1C8s0SVZT9mEZ8zHRWEiMrLnnGOoFa1FYGpW0+zNhYQ2rXVxdGNcGe5YNI/uxAAz9AKs0UUAFFFFABRRRQBW1Br1LGVtPjhkuwP3aTMVQn3I5rk5L34hFiG0bRgn96G6Z2/JlA/Wusv7aW7sZYILuW0kcYWeIKWT3G4EfmK8x8afaPCGi3Gq3XjjULh4+I7V2VTKx6LhNv50Abby+JH/wCPy1vhnr9nsbdwPxaTP6Vn3VpoU2f7Yu9XTPVZNNUD844z/OvnTVvH/iHVLppTfzQoT8sccjYH5kmun8C/E9bC6Wz8Q6TZ6pbyHCyyIokQ/XByPr+dOwrnsemaV8Nra8ha21Ix3O8FA97LFls8fKSAee2Kd8RbXW77VfO0+0uJrPTrICdIrdne4S4lCTLCenmCKNucMQH4AJBrS0rxGrzxxw+A9VtVZgPNEEQQA987gcfhXc0hnn+t+IJPBvhzQxoGkLb2SKZrjT5oCJYrOMAyuMP8rAMCd2SS3POa6bwxql3rFhd3lw1s8JvriK0a3UgNBHIUUkljuJKk5GAQRwKsXeg6dfakuoXMLyXC2z2nMz7DE/31KZ2nOBkkZ4HoKn0zTbPR9MttO0+AQWltGI4owSdqj3PJ+p5oAt0UUUAFFFFABRRRQAU11LxsodkJBAZcZHuM8U6igDFvPDx1CJYbzVb2eJXWQI8cGMqcj/lnV24sbieYyR6reW6n/lnEsRUf99IT+tXa4vX/ABJrum+M9N0O0TTXTVo5VtTIGLwtGEYySfMNy7fNwigElB8wycX7SRPKjqPsVx9l8n+1LvzN27z9sW/HpjZtx+Gfekt7G4gmEkmq3lwo/wCWcqxBT/3ygP61Db6zZnVk0OW9hl1dLbz5Y4o2UYG0M3UheXU7SxOGHXrWnS5mOxmnTbskn+3NQHsEg/8AjVTT2VxN5ezVLuDaoU+WsR3n1O5Dz9MD2q5RRzv+kg5UU47K4SCWNtUu5HfG2Vli3J9MIB+YNRxafdRyo7azfSKpBKOkGG9jiMH8jWhRRzP+kHKihNp9zJMzprF7ErHIREhIX2GYyfzNPeyuHt44l1S7R0zulVYtz/XKEfkBVyijmf8ASCyMubRFvLSe01C9uL62mTa0U6RbRzkH5UHIx3yPavB/jX4UsvCmlaZLYW8lxbzySLL57EJGwC7cBNoBOW656V9GVkeJ/Ddh4s0G40jUUzDMMq4+9Gw6MvuP5ZHempu//AE4nxBBdQwx7XsLeY5zvkaQH/x1gP0pUuI2vEkWxgx0EQaTbn1+9nP416ZrPwB8X2WoPFpkUGo2ufkmWZIyR7qxBB/Me5rrfh38B7my1KHVfFRiHkMHjsVIfcR/fI4x7DOe+O5d/wBWA9c8K2d4nh/SJrm/uy/2KIvbSLHtVjGMjOzdwfVs8ck1fbTbssSNbv1BPQJBx/5CrRoo53e/6IOVWKc9lcSiMJql3DsXaTGsR3n1O5Dz9MD2p9pbS2wfzb64ut2MecsY2/TYq/rmrNFLmdrDsFFFFSMKKKKACiiigAooooAKwL/wV4f1N5HvrF55JJxcM73EpbcAygBt2QmHcbB8nzHjmt+igDm7uy16TxzZalFbaadLtraW2Je7kEzCVoWZtvlleDFgDdznOR0rpKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooA/9k=""]"	若有需要，取重力加速度 $g = 10 m/s^2$ 及 重力常数 $G = 6.67 \times 10^{-11} N m^2/\mathrm{kg}^2$（若没有特别注明，取所有摩擦力为零）。
+21	PanMechanics_2024_18_2	"总质量为 $M$ 的弹性弹簧在未拉伸时具有均匀的质量分布。其弹簧常数为 $K$，为简单起见，假设其自然长度为零。现在它从顶端悬挂起来，并在恒定重力 $g$ 下垂直悬挂并达至静止状态。
+
+[figure1]
+
+如图 1 所示，在 $t = 0 s$ 时，顶端从静止状态释放，弹簧落下。为了理解它的下落运动，我们可以将弹簧建模为一系列 $N$ 个质量为 $m_N$ 的相同质量，与 $N - 1$ 个具有弹簧常数 $k_N$ 和零自然长度的相同弹簧连接。
+
+[figure2]
+
+如图 2 所示，坐标 $x_1, x_2, \cdots x_N$ 分别是距离底部 $(x_1)$ 和顶部 $(x_N)$ 位置的质量，从天花板开始测量（向下为正）。在 $t = 0 s$ 时，$x_N = 0 m$。"	求释放前处于平衡状态的弹簧的总长度 $L_0$。答案以 $M$，$g$ 和 $K$ 表示。		"[""\\boxed{$L_0 = \\frac{Mg}{2K}$}""]"	"[""Expression""]"	[null]	[2.0]	text+variable figure	Mechanics	PanMechanics_2024	"[""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"", 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""]"	若有需要，取重力加速度 $g = 10 m/s^2$ 及 重力常数 $G = 6.67 \times 10^{-11} N m^2/\mathrm{kg}^2$（若没有特别注明，取所有摩擦力为零）。
+22	PanMechanics_2024_18_3	"总质量为 $M$ 的弹性弹簧在未拉伸时具有均匀的质量分布。其弹簧常数为 $K$，为简单起见，假设其自然长度为零。现在它从顶端悬挂起来，并在恒定重力 $g$ 下垂直悬挂并达至静止状态。
+
+[figure1]
+
+如图 1 所示，在 $t = 0 s$ 时，顶端从静止状态释放，弹簧落下。为了理解它的下落运动，我们可以将弹簧建模为一系列 $N$ 个质量为 $m_N$ 的相同质量，与 $N - 1$ 个具有弹簧常数 $k_N$ 和零自然长度的相同弹簧连接。
+
+[figure2]
+
+如图 2 所示，坐标 $x_1, x_2, \cdots x_N$ 分别是距离底部 $(x_1)$ 和顶部 $(x_N)$ 位置的质量，从天花板开始测量（向下为正）。在 $t = 0 s$ 时，$x_N = 0 m$。"	应用牛顿第二定律，写出顶部 $x_N$、底部 $x_1$ 和第 $n$ 个质量 $x_n$ 的运动方程，而 $1 < n < N$，答案以 $m_N$、$k_N$、$g$ 以及其他质量的坐标 $x_2, x_3, \ldots$（如果需要）表示。		"[""\\boxed{$m_N \\ddot{x}_1 = -k_N (x_1 - x_2) + m_N g$}"", ""\\boxed{$m_N \\ddot{x}_n = k_N (x_{n+1} - 2x_n + x_{n-1}) + m_N g$}"", ""\\boxed{$m_N \\ddot{x}_N = k_N (x_{N-1} - x_N) + m_N g$}""]"	"[""Equation"", ""Equation"", ""Equation""]"	[null, null, null]	[2.0, 2.0, 2.0]	text+variable figure	Mechanics	PanMechanics_2024	"[""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"", 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""]"	若有需要，取重力加速度 $g = 10 m/s^2$ 及 重力常数 $G = 6.67 \times 10^{-11} N m^2/\mathrm{kg}^2$（若没有特别注明，取所有摩擦力为零）。
+23	PanMechanics_2024_18_4	"总质量为 $M$ 的弹性弹簧在未拉伸时具有均匀的质量分布。其弹簧常数为 $K$，为简单起见，假设其自然长度为零。现在它从顶端悬挂起来，并在恒定重力 $g$ 下垂直悬挂并达至静止状态。
+
+[figure1]
+
+如图 1 所示，在 $t = 0 \mathrm{s}$ 时，顶端从静止状态释放，弹簧落下。为了理解它的下落运动，我们可以将弹簧建模为一系列 $N$ 个质量为 $m_N$ 的相同质量，与 $N - 1$ 个具有弹簧常数 $k_N$ 和零自然长度的相同弹簧连接。
+
+[figure2]
+
+如图 2 所示，坐标 $x_1, x_2, \cdots x_N$ 分别是距离底部 $(x_1)$ 和顶部 $(x_N)$ 位置的质量，从天花板开始测量（向下为正）。在 $t = 0 \mathrm{s}$ 时，$x_N = 0 \mathrm{m}$。现在考虑 $N = 2$、$m_N = 1 \mathrm{kg}$ 且 $k_N = 1 \mathrm{N}/\mathrm{m}$ 的情况（$g = 10 m/s^2$）。"	求系统质心的加速度。（向下为正，单位用 $m/s^2$ 表示）		"[""\\boxed{10}""]"	"[""Numerical Value""]"	"[""m/s^2""]"	[2.0]	text+variable figure	Mechanics	PanMechanics_2024	"[""/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCADoAUYDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIhMUEGE1FhByJxFDKBkaEII0KxwRVS0fAkM2JyggkKFhcYGRolJicoKSo0NTY3ODk6Q0RFRkdISUpTVFVWV1hZWmNkZWZnaGlqc3R1dnd4eXqDhIWGh4iJipKTlJWWl5iZmqKjpKWmp6ipqrKztLW2t7i5usLDxMXGx8jJytLT1NXW19jZ2uHi4+Tl5ufo6erx8vP09fb3+Pn6/8QAHwEAAwEBAQEBAQEBAQAAAAAAAAECAwQFBgcICQoL/8QAtREAAgECBAQDBAcFBAQAAQJ3AAECAxEEBSExBhJBUQdhcRMiMoEIFEKRobHBCSMzUvAVYnLRChYkNOEl8RcYGRomJygpKjU2Nzg5OkNERUZHSElKU1RVVldYWVpjZGVmZ2hpanN0dXZ3eHl6goOEhYaHiImKkpOUlZaXmJmaoqOkpaanqKmqsrO0tba3uLm6wsPExcbHyMnK0tPU1dbX2Nna4uPk5ebn6Onq8vP09fb3+Pn6/9oADAMBAAIRAxEAPwD3+uU8R/8AIXH/AFwT/wBCaurrC1jR7q+vxPA0O3yghDsQcgk9gfWgDnKK1f8AhHNR/vWv/fxv/iaP+Ed1D+9a/wDfxv8A4mgDKorSh0K8uIUmhls5I3UMrrKxDA9x8tP/AOEc1H+9a/8Afxv/AImgDKorV/4RzUf71r/38b/4mj/hHNR/vWv/AH8b/wCJoAyqK1f+Ec1H+9a/9/G/+Jrnda1nR/D7FNS1zS4pR/yxWdpJP++FUn9KALtFYul65e63ciPTvDesSwnkXTwCGEj1DSFc/gK61PD2pMisRboSOVaU5H5LigLmZRWr/wAI5qP961/7+N/8TR/wjmo/3rX/AL+N/wDE0AZVFav/AAjmo/3rX/v43/xNH/COaj/etf8Av43/AMTQBlUVq/8ACOaj/etf+/jf/E0f8I5qP961/wC/jf8AxNAGVWr4c/5C5/64P/6EtH/COaj/AHrX/v43/wATV7R9HurG/M87Q7fKKAIxJySD3A9KAN2qmq/8gi9/64Sf+gmrdQXsLXNhcQIQGkiZAT0yRigDhqK1f+Ec1H+9a/8Afxv/AImj/hHNR/vWv/fxv/iaAMqitX/hHNR/vWv/AH8b/wCJo/4RzUf71r/38b/4mgDKorV/4RzUf71r/wB/G/8AiaP+Ec1H+9a/9/G/+JoAyqK1f+Ec1H+9a/8Afxv/AImj/hHNR/vWv/fxv/iaAMqitX/hHNR/vWv/AH8b/wCJo/4RzUf71r/38b/4mgDKorV/4RzUf71r/wB/G/8AiaP+Ec1H+9a/9/G/+JoAyqK1f+Ec1H+9a/8Afxv/AImj/hHNR/vWv/fxv/iaAMqitX/hHNR/vWv/AH8b/wCJo/4RzUf71r/38b/4mgDKorV/4RzUf71r/wB/G/8AiaP+Ec1H+9a/9/G/+JoA6DSv+QRZf9cI/wD0EUVJZQtbWFvA5BaOJUJHTIGKKAJ6KKKACsDxjNfp4emg022mnuLj91+6Ukop+8fy4/Gt+iqhLlkpWvYUldWOM+HM2oLorWl7azRwpiS2ldSFdG5wD9ef+Be1dnWb4d/5FnSv+vOH/wBAFaVXXlzVJO1iaatBIK8v+Jfjnxh4WvWXSNCWTTFiR31F4XlCkkgj5ThcYH3vWvUKKyLPH/D3h9fH9lFda18RbrU5XjV5NP0yZIEjyASroMk+nQV32h+A/C3h3a2maJaRTKcid03y59d7ZI/A1Q174X+FNem+1Ppwsr4EMt5YN5EqsOjcfKT7kGsL+yvid4RT/iV6naeKrJSP9Hvz5VyBnnDk4J92b6L2oEenUV5/YfFzQzerp3iC2vPDuo9DFqMe1Cf9l+6+jEKDXd211b3tslzazxTwSDKSxOGVh6gjg0DJaKKKAIbi6t7QRm5uIoRJIsSGRwu52OFUZ6kngDvU1eb/ABMk0k+JPCEOtTzW9kLi4uXliuZYzmOP5VURkEuXdcYG7ghepz2uqxXEGgvDYHUTNGqLGbN4nuCAQOGuCUJx1LkkjPfFAGnVHV9YsNCsGvdSuPJgDKgIVnZmY4VVVQSxJPQAmuVsP+Ej/tG28/8A4TLyfNTf9o/sjy9uRnf5fz7cddvzY6c0fExhb2vhvUJQVs7HXra4upcfLFHh13t6KGZefegDqNG1zTtfs3u9MuPOiSVoZAyMjxyKcMrIwDKw9CAeRWhXE+AXhvtU8V6vYqP7NvdTBtpFOVm2RIjyKe6lw3I4ODXbUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFADZJEijaSR1REBZmY4AA6kmmwTxXNvHcW8qSwyqHjkjYMrqRkEEcEEd65L4qSrD8M9bLbsPEsWVkZNpd1TcSpHA3ZIPBAIORkVr+FINJg8PW40O4nuNOORDJNPLLkL8nymQk7fl4x8uORwaANS0u7a/tY7qzuIbi3kGUlhcOjD1BHBqSSRIo2kkdURAWZmOAAOpJrza6httYu5LvwFp17b3srbm1a3f7JZSH5uXDKy3HPdY2/3hXUa9Z6pcfDfVbKdlu9Vk0qeIm3jKiWUxMPlXJ6mgCfRPGGheIrprbTL0yzLCLgJJBJEXiJwJE3qN6543LkdPWtyvK/CN/Y674p8JyaSyzf2Z4faO/ljziJm8pUib0YFHO0816pQAUUUUAFFFFABRRRQBm+Hf+RZ0r/rzh/9AFaVZvh3/kWdK/684f8A0AVpVdT42TH4UFFFUtR1fTdIgM+paha2cQ/juJVQdcdzUFF2ivPbz4vaNJM9r4b0/UvEd2p27dPt2MYP+1IRgD3AIpsw+KHiG4jaE6d4TtAMOpZb6Yn1+6F/WgDstcstGv8ATXh12Gzlsj94XYXYPfJ6H3rw3VP+Ed8OXNxN8NfE+rf2ruGNKtElurdiTg5BUj16lq9DtPhHosl4L7xFeX3iC83bi19KREG9RGuAPociu20/S9P0i2FtptjbWcAOfKt4ljXPrgACgDmfAGreL9T0+T/hK9GWydQDDOCFMo77o8kqffjPoK7GiigAooooAKKKKACiiigAooooAKKKKACiiigAooqjrOpf2Pot5qItZ7r7NE0vkQLueTA6AUAXqK8g0v4q6/4w1iTSNB0zTdLnQHfJqtwxI5AG1VAy3PSum/4QnxBqgA8QeNtQljIw0GmRLZqR6EjJP6UAdTqmvaTokJl1TUrWzQDP76UKT9AeT+FY+mfELw3rThdMuL68Gcb4NMuXQf8AAhHgD3zTdM+HHhLSiXj0W2uJm+9NeDz5G/F8/pXUIixoqIoVFGAqjAAoFqKDkAjPPqMUtFFAwooooAKKKKACiiigAooooAKKKKACiiigDN8O/wDIs6V/15w/+gCtKs3w7/yLOlf9ecP/AKAK0qup8bJj8KCuB8efCnS/G919va7mstSWNY1nVRImATjKHHr2I6DOa76ioKPL7OT4l+CtOitptJ0zxLYQDYhsZTBcKgHGVK4P0UE1qab8XfC1zdrYanLc6FqJHzW2qwNAV4ycsflA9yRmu8qjqujaZrlobXVLC3vID/BNGGx7j0PuKALcM0VxCk0MiSRSKGR0YFWB5BBHUU+vNpvhKdMuEn8GeJtT8PYbc1vva5t2467HYc/7xYe1Z17458deA3j/AOEw0ez1TTCyxLqOmtsdie5Q9WxnjCDjgmgD1qiuX8H/ABA0HxvDKdKmkW4hGZbWdQskYzjJAJBH0JrqKACiiigAooooAKKKKACiiigAooooAKKKKACiiigDH1vwroPiOMpq+k2l3kY3yRjeB7MPmH4GuYf4f6toq7/B/iq9sVXJ+xX5+1W59hu+ZPrz9K7+igDzweMvGPh9pF8U+EJLm2Q4F9obiZTxnJjYhlUc5Y4+lb/h/wAe+GfExSPTdWga5b/l1lPlzA+mxsE/hkVuXl9aadAZ726htoQceZNIEXP1NeZeKda+G/iSURNpc2vXzEhX0i2Zpgw9JFK9PrigD1WivGtE0n4lWusf8SNrmz0Jdvk2/iG4SVtg6qdhdh9OPrXsce/y18wKJMDcFORnvigB1FFFAHOeOtSvNI8H3l7p85gukkhVJQqsVDTIp4YEdGPUVyfgDxNruq+KnstS1OS7t/sUkoR4YlwyvGAcogPRjXRfEv8A5EK+/wCu1t/6UR1xPwx/5Hhv+wbN/wCjIa7qUIvDTk1qv+Ac85NVoq+h7HRRRXCdAUUUUAFFFFABRRRQBm+Hf+RZ0r/rzh/9AFaVZvh3/kWdK/684f8A0AVpVdT42TH4UFMmmit4WmnlSKJBlndgoA9yafXnHj/4Raf421B9WW/mtdS8lY13qJITtJwSvBB5xw2OmQeQYKNDVvi34L0kBRrEd/O3CQaeDO7nOMAr8oP1Iqj/AMJ54q1sGPw14Gv4t33brWj9mjUeu3q34GsfQ5PFXw00+Gyu/BFrqVjGoU32gtumxznejKGc55zhQK7LQ/iT4S8QsIrPWIUuM4NvcgwyBu4w+Mke2aAMYeGfiFrahdc8XW+l25OWh0WAhz7ea3I/AGrNn8IvC0UouNSS+1u7H/Lxql28zfTGQpH1Fd3RQBUsNL0/SofK0+xtrSP+7BEqA/kKt0UUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFVdRv4NL025v7nf5FtG0smxCx2gZOAOTVqigDzC2+LzeI9Qk03wj4fnvrxRndezpbIB3OCSxxzxjtWlDonxD1cyNrHiex0iF/lFvo9t5jbe/wC8k5VvpmtjWfh/4V164Fzf6NAbkHP2iAtDIT6lkIJ/GsRvBHinRnaXw142u2THy2esp9qjPsH4ZR9ATQBbsPhZ4ZtiJL6K61efOTLqdy0xJ9dpO39K7C2tbezgWC1gighX7scSBVH0ArhY/F/i7Q38rxR4Se4iUMWv9DYzJx/0yb5lGO+SeOla2jfEfwlrpKWmtWyTj70Fy3kyA5xja+P0oA6migEEAg5B6GigAooooA88+KT66mkFIUtZNEdozcuImM0JR1cHO7G0lQCccfqOK8Hya0viqI+H47aS5aBopmuY2eOKJmQlztYYPyDA7/qPd3RZEZHUMrDBUjII9Kz9H0HTNAt5INLs47aORzI4XPJPuew6AdhwK6qeJ5aLp23MZUuaanc0EDBFDkFsckDAJ+lLRRXKbBRRRQAUUUUAFFFFAGb4d/5FnSv+vOH/ANAFaVZvh3/kWdK/684f/QBWlV1PjZMfhQUUUVBQVgeIfBPhvxSjf2xpFrcSkAefs2yjHTDj5se2ce1WtV8TaFoaFtU1eytMdRNMqt+Wc1yn/C29IvppYfDuk6zr7Rjl7C1/dg+hZiMfkaAKA+G3ifw9j/hDvG95DbrytjqaCePPoDj5V9gv40h+JuveFwI/HXhK6twzbY73S8TwOc9wW+XoTgkk+lXI7/4pa5PmHSdH8OWn968mN1MR7BDt/A4pzfDK61YsfFPi/VtWQyCT7NCFtoMjp8gyfxBFNAdXoHinQ/FFs0+i6lBeKmN6ocOmem5Dhl/EVr1i6F4S0Lw0XbSNPS2d1CO4dmZgDnBLEnrW1SAKKKKACiiigAooooAKKKKACiiigAooooAKKKpas2oppF02kJbvqIjJt1uc+Wz9g2MHFAF2mu6xoXdgqjqWOAK8P1LxB8R7fWkj8WXNzoWj7CZbvRrATRjpyXO8rjkkkj2Fb3h/wR8PvFO67/tq88UTDDM17qTu6445QFcDjuKAOsv/AIjeENOuWtp9dtXuBx5UBMzZ9MIDzXM63qVl4zhW3i+HGo6vE+SlzeRrZqPdZGO9fqADXfaZoWk6NEsWmaba2iAYxDEq/mR1rQoA8W8PfDXx5pd6s9j4jGi2fml1sftD3aRqf4SpAVvqeeK9miDrEiyuHkCgMwXaGPc45xT6KACiiigAooooAKKKKACiiigAoorE8NeJYvE9pc3MFhe2iW9y9sftQjG50OG27HYEA5GfUUAbdFFFAGb4d/5FnSv+vOH/ANAFaVZvh3/kWdK/684f/QBWlV1PjZMfhQV5/wDEDwV4m8S3sdzofimbT4VgEbWXmSRRuwLHcWQ55DYIwfuivQKKgo8F8PaFb+B4ox4s+HNxfTK7NJq8AW+B+Y4Yp1UD1wD7V6joHxC8H+IJFtdI1u1eUfKkDhoWOB/CrhSfwFdTXPa54F8L+IxIdV0Oznlk+9MI9kp7/fXDfrTbuB0PUZFFeat8MdW0KD/ijPGOqWDA5FrfMtxbn2AI+X64Oaral488beCreOTxV4ZtL2yDLG2o6bd4BJ7+Wwzk/gM0gPU6K5nwn490Hxmso0qeUXEIDS288ZSRAeM+hGe4JrpqACiiigAooooAKKKKACiiigAooooAKKKKACiiigArltd+HPhXxDKbi70mGK83Fxd2v7mYN/eLLjcf97NdNNNFbxmSaRI4x1Z2AA/E1ymq/E7wbpBKTa9aTTDgQ2ree5PphM8/WgDNHhLxjoDbvDni172Aciz1xPOGAOnmrhh3pP8AhOvEegrnxZ4PukhwSbzSD9qjUDu6/eQe5qwfHesagANC8D61cErnzL7ZZoM9CC5+b8KlW3+Impwx+ff6LomTlvs0LXUgHpl8Ln8DQBp6F468L+JZPK0nWrW4mwD5O7ZIforYJ/CuhrzkfBvQry9lv9burrU7yaRpZHbbEpY9SFUcH8a9DijWGJIkztRQoySTge5603YB9FFFIAooooAKKKKACiiigCpql42n6Vd3kdvLcPBC0iwwoXeQgZCgAEkk8V5toHieXwj8P4LZdF1OR9O0iW+vJ7y0mtkFxkMYgXQbyXkbJBwApPPSvVKhvLSC/sp7O6iWW3uI2iljbo6MMEH6gmgDA8M6zql5qms6RrAs3u9NeH99ZoyRuskYYDazMQQcjrzxwK6WszRfD+meHoJYtNgeMTOHkaSZ5XchQoy7ksQAAAM4AHFadAGb4d/5FnSv+vOH/wBAFaVZvh3/AJFnSv8Arzh/9AFaVXU+Nkx+FBTJZooF3SypGPV2Ap9cP47+GWn+Oporm51C8triGMRxhGDw8EkFoz1PPYjPFQUWdV+KHg3SQyya7bXEwO0Q2bee5PphM8/XFZreOvFOqpnw74D1Aoek2qyJarj1Ck5NZGj6F4w+HVstrpXh3RNdsYwSJrY/Zbog5J3FywY+mM+la1j8YfD5uWstet7/AMP3q9YtRt2UfUMARj64oAcfD/xC1vadW8VWmkQHlrfR7bL/AE81+R+FWLb4U+Gx8+qNqOtXG7cZtSvZJCT/ALoIUj6iuvstQs9St1uLG7guYWAIeGQOCD7irNAFWy0yw01NljZW1quMYhiVBj8BVqiigAooooAKKKKACiiigAooooAKKKKACiiigAqtqNq99pl1aR3Mtq88LxrPCcPEWBG5T2IzkfSrNFAHi+pfB7XTq1rqEusp4nhhZnkstXmkj8zjoGBcZ9OAK2rXxdZeCYWTVPh9e6ChPzz6fbxz2+P7zSR4/IjNenUU2wOf0Xxx4X8QrH/ZeuWU0kn3YTJsl64/1bYYflXQVg6z4K8M+IJDJqmiWdzKTkymPa5PuwwT+dcTqOk6J4PmkbSviNPoku7b9jurlLyJfYQud360gPVKK8Y0D4l+NJb+e2XQl8S2kL7Re2MEkAceuWG38OPrXskMhlgjkaN4y6hij43LkdDgkZHsaAH0UUUAFFFFABRRRQAUUUUAFFFFABRRRQBm+Hf+RZ0r/rzh/wDQBWlWb4d/5FnSv+vOH/0AVpVdT42TH4UFFFch4u+JXh/wXfR2Wqm7a5lh86OOCAvuXJHB4GcqeM1BR19V7yxtNRtmtr21huYG6xTRh1P4HivNdN+KWveLRP8A8Ij4Qa5SFlV5r29jiCZHdQc59s1o/wBhfEfWGDan4nsNJiJ3eVpVuWYexaTr/KgBNS+D3heSdr3SpL3QLvk+dptyYhntkdMewxXL6x4m8Z/Dzy3l8SaR4msWZYlimUR3I/74/md1dY3wk0O9n87W9Q1nWWYhnS9vWMbH12rgD6V0uneEfDmkKosND0+AqMB1t13Y/wB7GT+dCAzfBvjYeLEkV9Ju7CaJAzeYQ8Tc4O114OD2IB9q6ukVVRQqgKoGAAMACloAKKKKACiiigAooooAKKKKACiiigAooooAKhvLqOxsp7uUO0cEbSMI0LsQBk4A5J46CpqKAPKV+NkWqapDpnh7w3eXd3KxUfbbiO0QADOcnd+oHpW6tn8SNWcG61PRtBg/uWcDXcp9iXwo/DNdLq/hzRdfiaPVdLtLwMu0mWIFgM54bqPwNcvcfDKO0Bfwv4h1fQpdwYRpcNPASP70bk5+gYCgCeP4cQXLbtd1/XNY9Yp7sxxf98x7f51taV4O8N6IE/s7RLGB0O5ZBCC4PrvOW/Wub834n6Ezb7fRvE1svCmNzZXDe5Byg+goh+K1hZ4TxPouseHpMffurVpIWOcYV0Bz9SAKAO/orO0rXtI1yLzdK1O0vVxuPkTK5A9wDkfjWjQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQBm+Hf+RZ0r/rzh/8AQBWlWb4d/wCRZ0r/AK84f/QBWlV1PjZMfhQVT1HStP1e3NvqNjb3cJ/gniDj9auUVBRwtz8KdEQySaJe6voMzjDNpt/Igf03Ak5A9Biq0eh/EnQY410/xNYa7Cg5i1S2MchHoHQ5J92Ndze6lY6bEZb68t7aMDO6aQIP1rlJ/ix4OSdbe11J9RuG4WKwt3mY/iox+tAGfN8Rtb8PwLJ4r8F6haxD791p8i3MSjOATgjHbrW3o3xJ8Ia66x2euWyzt/yxuCYXz6YcDP4ZrNbxv4l1AyJongTUWw2Em1KVbVSPXBycVh+Ifhx4g8d3EUmvtoOnJGNwaxgeWYsf7zMVBosB6wCCMg5FFcb4H+HsHgnzDBrGo3fmpsaKaT9yDnO5U7Ht16GuyoAKKKKACiiigAooooAKKKKACiiigAooooAKKKgvbOHULC4srhS0FxE0UgDEEqwIPI5HBoAr6hrelaUpbUNStLUDk+dMqn8ia5yf4peE0cxWd/Lqc4bb5On28k7E/VRj9a5DUfgBppuRc6RrNxbupBC3kQuBkc4yCpx9c10ME3xF0OUJ/YHhzUrLB+TTJWtGU++/IP0H50AWj4w8S30bnSPAt+SGwr6lcR2qkeuMlvwx+NJDB8RtTDrfyeGdOtZP+WS28t24Ho2XVTSj4kW9mUXXdA1zSCSQZJrQyRDHffHkY/CtnSfGfhrXMDTdcsbhycBBMA5P+6cH9KAOMsfgrpsWoS319qtxNcStvc2sKW4B/wBnGSo9gfTmvTYYhDBHEHdwihdztuY4GMk9z70+ii4BRRRQAUUUUAFFFFABRRRQAUUUUAFFFFAGb4d/5FnSv+vOH/0AVpVm+Hf+RZ0r/rzh/wDQBWlV1PjZMfhQVwnj7wn4q8RTwvoPiZ9Pt/KEc1pvaNXOSd29QW5BAx7Zru6Kgo+f9E8JyeF79pvGXgXUNdcHdHfwS/bAijPBQtyO/PPtXovh/wAe+ACyWun3FnpUzkr9nmt/sjAjscgD9a7us7VdA0jXIvL1TTbW8GNoM0QYgdeD1H4UAXYLiG5iEtvNHLGejxsGB/EVJXm2qfDfwlpO6fTdYuPC8+dyyW1+Ykz7qxwR7cVyF58QfEXha+tbXTfFOleLrWQ45hzKOeQWjbr6daAPeKK4/wAE+M7/AMUq6X/hu/0uSNN3nSLmCQggEKxwc85xjsea7CgAooooAKKKKACiiigAooooAKKKKACiiigAooqC+hmubC5gt7lraeSJkjnVQxiYggMAeDg849qAJ6y9S8SaHo5I1LWLC0YDJWa4VW/InNeSa78MvH1zM00/iOXXLcud9q17Jbean93aPkGa0dNg8JeGIUXU/hhe6cynLTvZrqCR+5mBY4oA6xvih4akVTpsl9qzM20Jp9lJKSfrgD9awNV06DxS9zKvwqWV3OTdag8VnK7Y6krmSun0X4g+C9TgjTTte05F+6kLyCFvoFbB/IV1KsGUMpBUjII70AeN+H/hb420mZTa+MX0m2zuW3hke5VO+3Y4CEfhXsFrHNFaQx3E3nzIirJLsC+YwHLYHTJ5xUtFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFAGb4d/5FnSv+vOH/ANAFaVZvh3/kWdK/684f/QBWlV1PjZMfhQVxPjvxnrPhQxf2d4YudUieIs1yhOyNs4wwAJ6c121FQUeIeGviN4o8Zarc2n9t6HoAiUMUlhLOc9Nu8gEjvXWp8O9Xv5A2tePdZvYGGTFbYtVP4oeldVrHhTw/4gRl1XR7O6LdXkiG/wD76HP61yU3wktbSUS+GvEOs6E6tuWOG4MkK/8AAGP8zRZCNG3+E/gyGRJZtI+2Tqc+bdzvKx+uTj9K6mx0vT9Mj8uwsba1Q8lYIlQH8hXCxp8UvD8DM0ukeJYl6Kc20+PXIG0/Soo/jDa6eEj8VeHtX0KdgCPMhMkZHqGHP6UDPSqKzNG8RaN4ht/P0jUra8TGT5TglfqOo/EVp0AFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFRXKSyWsqQTeTMyERyld2xiODjvg84oAlprukaF3ZVVRksxwBXi/iTwl8XJEZ4fEi6ig4ENnP8AY2b6jAH/AI9VaSPwLZpCnjTwp4mgliAV73VBPcRbu+HRyD+AoA7fxFrPwuujLJrl54bupfuuzGKaUY7fLlq4OMeCWuJX8BS+LYZ2zg6JFM0G/wBXVxgj9K7/AMKat8NrhIU8Oz6KkoOI02rHOfwcBzXc0eoHkHh6++MUe03Fhb3kO4qRqXlQvj1zGc/oa9atmme1ha5jSOcopkRG3KrY5APGRnvUtFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFAGb4d/5FnSv+vOH/0AVpVm+Hf+RZ0r/rzh/wDQBWlV1PjZMfhQVka14p0Lw7tGr6rbWbMu9Vlf5mGcZA6nmtesbXfCeg+JjEdZ0yC8aEFY2fIKgkE4IIPYVBRy0fxi0C+ne30bT9a1adRkx2dkScevzEcVMfE/jnVNjaR4MWziPWTVrlUI/wCAKc1W/wCFRWGm3j3vhjWtT0O7bjMbiaPHptfqPqankh+J2kjNvdaJrkSgKEmja3lf/aJHy5oAkGjfETUN5vPFGm6ajdEsLHzSv/AnNI3wws9ReCTxFrWq61JEchZ5Qkf/AHyoGPzph+IGtaWwTxB4I1a3AA3z2BW7jH4rgirth8VPBl/MkA1qK2uG48q7RoWU+h3AAfnRewWNXRPB3h7w3cST6RpcFpNIux5EyWYZzgkk1uVHBPDcxLLbyxyxt0eNgwP4ipKACiiigAooooAKKKKACiiigAooooAKKKKACiimTLI8EixSCOQqQjldwU44OO/0oAfRXjHiLRvjRJErx6rZzgf8s9LmWFhxznzFXP8A31/hVezbRogg8caf45idUxPJfyzzWhfp8piY5z9MUAdv4j074aTh5Nej8Pq6nLM7xxyE+5BDGuJnl8H205Xwf4z8SW9yo/dWWmrPeQk9hsKMMfjXVeHrn4UMVTSToCSjkLOqpLn6SANmvQYjEYlMJQx4+XZjGPbFAHkHh/xJ8W3kMknh0alabsZu40sZceuGYY/75NevW7yyW0TzxeTMyAvFu3bGxyMjrg8ZqSigAooooAKKKKACiiigAooooAKKKKACiisHxdc6pY6DJe6VKElgIeQFA25O/UduD9AaqEeeSiuopPlVy54d/wCRZ0r/AK84f/QBWlXHfDy61W90cy3soNpEFgtU2AcKME5xz2H4Guxq68OSo0yacuaKYVy/i3x7o/gt7ddVjvT9oUlGt7cyLwQME9Aea6imyRpLGUkRXQ9VYZBrIs8psvjdFrWsrpuieG7u6eQ7Y2muEh3H6c4rejvviZfIwXRtB0wngNcXTzEe+EGK1dS+H/hXVJfNuNFtlmHSWAGFwfXKY5rMPw8ubOEJovjHX7Ihs4mnFyn0w4/rQLUbb6J8Rbg5v/F2nWo9LLTg/wCr1Ruvg3pOsXTXuv6rqGoXrnLSqUiB/wCAhavmP4laVG/lzaJrqg/L5qtbSkfh8tNfx9q+lsf7e8E6tbQom6S4smW6jX1J24OKNgNfwz4E8P8AhGSSTRrRoJJE8uRjKx3DOeRnGffFdJXP+G/GuheKi6aXdlriNd0lvLG0cqDOMlSOma6CgYUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUhIVSzEAAZJPalprokkbRyKrIwIZWGQQexFAGLfeMvDOmwNNd6/psSL63KE/gAcmsl/in4QCoYNRmuy/3VtbOaUn/vlaq6h8G/A98jbNI+xyMc+ZaStGR9Bkr+lJY+A9e8PW6WvhrxjNBZIS32bULGK4BJ/wBpdhAoEVNU8SaPq+9H+HGuap5vHmSaQiq31ZyCPrXNXHg/VbmD/inPBF94buXPyXSa6I1X/ejUt+grtvtfxK0+TdPpfh/V4c4C2VxJbS49f3m5f1p58fXNnvGreD/ENpsGWeGBbmMD/ejY/wAqBnOaH4W+LOnnZP4u05ouuJt10T7EtGp/WvUrfz/s0X2kxm42DzDECFLY5xnnGa5uy+JHhG+nSBNbghuH6Q3QaB/ycCuoVldQysGVhkEHIIoAWiiigAooooAKKKKACiiigAooooAKa6LJGyOoZGBDKRkEHtRRQBFZWcGn2cVpaxiOGJdqKOwqeiim227sNgooopAFFFFABRRRQAwQxCYzCJBKRtL7RuI9M0+iigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigCpe6Xp+pLtv7C1ul9J4VcfqKsRRR28KQwxpHFGoVERQFUDgAAdBRRQA+iiigAooooAKKKKACiiigD/2Q=="", 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""]"	若有需要，取重力加速度 $g = 10 m/s^2$ 及 重力常数 $G = 6.67 \times 10^{-11} N m^2/\mathrm{kg}^2$（若没有特别注明，取所有摩擦力为零）。
+24	PanMechanics_2024_18_5	"总质量为 $M$ 的弹性弹簧在未拉伸时具有均匀的质量分布。其弹簧常数为 $K$，为简单起见，假设其自然长度为零。现在它从顶端悬挂起来，并在恒定重力 $g$ 下垂直悬挂并达至静止状态。
+
+[figure1]
+
+如图 1 所示，在 $t = 0 s$ 时，顶端从静止状态释放，弹簧落下。为了理解它的下落运动，我们可以将弹簧建模为一系列 $N$ 个质量为 $m_N$ 的相同质量，与 $N - 1$ 个具有弹簧常数 $k_N$ 和零自然长度的相同弹簧连接。
+
+[figure2]
+
+如图 2 所示，坐标 $x_1, x_2, \cdots x_N$ 分别是距离底部 $(x_1)$ 和顶部 $(x_N)$ 位置的质量，从天花板开始测量（向下为正）。在 $t = 0 s$ 时，$x_N = 0 m$。现在考虑 $N = 2$、$m_N = 1 \mathrm{kg}$ 且 $k_N = 1 \mathrm{N}/\mathrm{m}$ 的情况（$g = 10 m/s^2$）。"	求出两个质量随时间变化的距离函数：$d(t) = x_1(t) - x_2(t)$。(表达式中重力加速度用 $g$ 表示)		"[""\\boxed{$d(t) = g \\cos(\\sqrt{2} t)$}""]"	"[""Expression""]"	[null]	[5.0]	text+variable figure	Mechanics	PanMechanics_2024	"[""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"", 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""]"	若有需要，取重力加速度 $g = 10 m/s^2$ 及 重力常数 $G = 6.67 \times 10^{-11} N m^2/\mathrm{kg}^2$（若没有特别注明，取所有摩擦力为零）。
+25	PanMechanics_2024_18_6	"总质量为 $M$ 的弹性弹簧在未拉伸时具有均匀的质量分布。其弹簧常数为 $K$，为简单起见，假设其自然长度为零。现在它从顶端悬挂起来，并在恒定重力 $g$ 下垂直悬挂并达至静止状态。
+
+[figure1]
+
+如图 1 所示，在 $t = 0 s$ 时，顶端从静止状态释放，弹簧落下。为了理解它的下落运动，我们可以将弹簧建模为一系列 $N$ 个质量为 $m_N$ 的相同质量，与 $N - 1$ 个具有弹簧常数 $k_N$ 和零自然长度的相同弹簧连接。
+
+[figure2]
+
+如图 2 所示，坐标 $x_1, x_2, \cdots x_N$ 分别是距离底部 $(x_1)$ 和顶部 $(x_N)$ 位置的质量，从天花板开始测量（向下为正）。在 $t = 0 s$ 时，$x_N = 0 m$。现在考虑 $N = 2$、$m_N = 1 \mathrm{kg}$ 且 $k_N = 1 \mathrm{N}/\mathrm{m}$ 的情况（$g = 10 m/s^2$）。"	当两个质量碰撞时（设碰撞时间为 $\tau$），设底部质量从 $t = 0 \mathrm{s}$ 的下降距离为 $D_2 = x_1(\tau) - x_1(0) = \gamma L_0$。求 $\gamma$ 的数值。		"[""\\boxed{0.117}""]"	"[""Numerical Value""]"	[null]	[6.0]	text+variable figure	Mechanics	PanMechanics_2024	"[""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"", 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""]"	若有需要，取重力加速度 $g = 10 m/s^2$ 及 重力常数 $G = 6.67 \times 10^{-11} N m^2/\mathrm{kg}^2$（若没有特别注明，取所有摩擦力为零）。
+26	PanMechanics_2024_18_7	"总质量为 $M$ 的弹性弹簧在未拉伸时具有均匀的质量分布。其弹簧常数为 $K$，为简单起见，假设其自然长度为零。现在它从顶端悬挂起来，并在恒定重力 $g$ 下垂直悬挂并达至静止状态。
+
+[figure1]
+
+如图 1 所示，在 $t = 0 s$ 时，顶端从静止状态释放，弹簧落下。为了理解它的下落运动，我们可以将弹簧建模为一系列 $N$ 个质量为 $m_N$ 的相同质量，与 $N - 1$ 个具有弹簧常数 $k_N$ 和零自然长度的相同弹簧连接。
+
+[figure2]
+
+如图 2 所示，坐标 $x_1, x_2, \cdots x_N$ 分别是距离底部 $(x_1)$ 和顶部 $(x_N)$ 位置的质量，从天花板开始测量（向下为正）。在 $t = 0 s$ 时，$x_N = 0 m$。现在考虑 $N = 3$ 的情况。"	为了使弹簧的总质量和总弹簧常数 $K$ 与 $N = 2$、$m_N = 1 kg$ 且 $k_N = 1 N/m$ 的情况相同，（1）求出对应的 $m_N$（单位用 $kg$ 表示），（2）求出对应的 $k_N$（单位用 $N/m$ 表示）。		"[""\\boxed{2/3}"", ""\\boxed{2}""]"	"[""Numerical Value"", ""Numerical Value""]"	"[""kg"", ""N/m""]"	[1.0, 1.0]	text+variable figure	Mechanics	PanMechanics_2024	"[""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"", 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""]"	若有需要，取重力加速度 $g = 10 m/s^2$ 及 重力常数 $G = 6.67 \times 10^{-11} N m^2/\mathrm{kg}^2$（若没有特别注明，取所有摩擦力为零）。
+27	PanMechanics_2024_18_8	"总质量为 $M$ 的弹性弹簧在未拉伸时具有均匀的质量分布。其弹簧常数为 $K$，为简单起见，假设其自然长度为零。现在它从顶端悬挂起来，并在恒定重力 $g$ 下垂直悬挂并达至静止状态。
+
+[figure1]
+
+如图 1 所示，在 $t = 0 s$ 时，顶端从静止状态释放，弹簧落下。为了理解它的下落运动，我们可以将弹簧建模为一系列 $N$ 个质量为 $m_N$ 的相同质量，与 $N - 1$ 个具有弹簧常数 $k_N$ 和零自然长度的相同弹簧连接。
+
+[figure2]
+
+如图 2 所示，坐标 $x_1, x_2, \cdots x_N$ 分别是距离底部 $(x_1)$ 和顶部 $(x_N)$ 位置的质量，从天花板开始测量（向下为正）。在 $t = 0 s$ 时，$x_N = 0 m$。现在考虑 $N = 3$ 的情况。"	求解底部质量随时间变化的位置：$x_1(t)$。提示：尝试先找出质心的运动方程，$x_1$ 和 $x_3$ 之间的差的运动���程，及另一个由 $x_1, x_2$ 及 $x_3$ 的线性组合组成的量的运动方程。		"[""\\boxed{$x_1(t) = \\frac{5}{9}g + \\frac{1}{2}gt^2 + \\frac{g}{2} \\cos(\\sqrt{3}t) - \\frac{g}{18} \\cos(3t)$}""]"	"[""Equation""]"	[null]	[8.0]	text+variable figure	Mechanics	PanMechanics_2024	"[""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"", 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""]"	若有需要，取重力加速度 $g = 10 m/s^2$ 及 重力常数 $G = 6.67 \times 10^{-11} N m^2/\mathrm{kg}^2$（若没有特别注明，取所有摩擦力为零）。
+28	PanMechanics_2024_18_9	"总质量为 $M$ 的弹性弹簧在未拉伸时具有均匀的质量分布。其弹簧常数为 $K$，为简单起见，假设其自然长度为零。现在它从顶端悬挂起来，并在恒定重力 $g$ 下垂直悬挂并达至静止状态。
+
+[figure1]
+
+如图 1 所示，在 $t = 0 s$ 时，顶端从静止状态释放，弹簧落下。为了理解它的下落运动，我们可以将弹簧建模为一系列 $N$ 个质量为 $m_N$ 的相同质量，与 $N - 1$ 个具有弹簧常数 $k_N$ 和零自然长度的相同弹簧连接。
+
+[figure2]
+
+如图 2 所示，坐标 $x_1, x_2, \cdots x_N$ 分别是距离底部 $(x_1)$ 和顶部 $(x_N)$ 位置的质量，从天花板开始测量（向下为正）。在 $t = 0 s$ 时，$x_N = 0 m$。
+
+(f) 考虑 $N = 2$、$m_N = 1 \mathrm{kg}$ 且 $k_N = 1 \mathrm{N}/\mathrm{m}$ 的情况（$g = 10 m/s^2$）。当两个质量碰撞时（设碰撞时间为 $\tau$），设底部质量从 $t = 0 \mathrm{s}$ 的下降距离为 $D_2 = x_1(\tau) - x_1(0) = \gamma L_0$。求 $\gamma$ 的数值。
+注意：(f) 是前置问题，请不要写入最终答案中。
+
+现在考虑 $N = 3$ 的情况。"	"底部质量经过 (f) 部分中的 $\tau$ 时间后：
+
+（1）求下降的距离 $D_3 = x_1(\tau) - x_1(0)$（用 $L_0$ 表示）。
+（2）比较 $D_3$ 及在 (f) 部分所得距离 $D_2$，看看哪一个比较小，在答案中写上 $D_3$ 或 $D_2$。"		"[""\\boxed{$D_3 = 0.054 L_0$}"", ""\\boxed{$D_3$}""]"	"[""Expression"", ""Open-Ended""]"	[null]	[1.0, 1.0]	text+variable figure	Mechanics	PanMechanics_2024	"[""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"", 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""]"	若有需要，取重力加速度 $g = 10 m/s^2$ 及 重力常数 $G = 6.67 \times 10^{-11} N m^2/\mathrm{kg}^2$（若没有特别注明，取所有摩擦力为零）。