AP-Style Practice QuestionsAP风格练习题
Topics主题 7.1 - 7.5MECH
Show all supporting work on scratch paper. Each item is labeled with its Mechanics topic and whether a calculator is permitted on that AP Exam section. Take $g = 9.8~\mathrm{m/s^2}$ unless a problem says otherwise.请在草稿纸上展示所有辅助计算过程。每道题均标注了对应的力学主题，以及该AP考试部分是否允许使用计算器。除非题目另有说明，取 $g = 9.8~\mathrm{m/s^2}$。
A $0.50~\mathrm{kg}$ block on a frictionless horizontal surface is attached to a spring of force constant $k = 200~\mathrm{N/m}$ and oscillates in SHM. The period of oscillation is closest to一个 $0.50~\mathrm{kg}$ 的滑块在无摩擦水平面上与弹簧常数 $k = 200~\mathrm{N/m}$ 的弹簧相连，做简谐运动。振动周期最接近
A simple pendulum of length $L = 1.0~\mathrm{m}$ swings with small amplitude in a region where $g = 9.8~\mathrm{m/s^2}$. The period of the pendulum is closest to一个摆长 $L = 1.0~\mathrm{m}$ 的单摆在 $g = 9.8~\mathrm{m/s^2}$ 的区域内以小振幅摆动。该单摆的周期最接近
An object undergoes simple harmonic motion when the net force on it is当作用在物体上的合力满足以下条件时，物体做简谐运动：
A block on a horizontal spring oscillates in SHM with amplitude $A$. At the moment the block is at $x = +A$, its energy is一个滑块在水平弹簧上以振幅 $A$ 做简谐运动。当滑块位于 $x = +A$ 时，其能量为
A particle in SHM has position $x(t) = A\cos(\omega t)$. Its velocity at $t = 0$ is一个做简谐运动的质点，其位置为 $x(t) = A\cos(\omega t)$。在 $t = 0$ 时刻，其速度为
A $0.20~\mathrm{kg}$ block on a horizontal spring of force constant $k = 50~\mathrm{N/m}$ oscillates with amplitude $0.10~\mathrm{m}$. Its maximum speed is closest to一个 $0.20~\mathrm{kg}$ 的滑块在弹簧常数 $k = 50~\mathrm{N/m}$ 的水平弹簧上以振幅 $0.10~\mathrm{m}$ 振动。其最大速度最接近
The length of a simple pendulum is increased by a factor of $4$ while $g$ is held constant. Compared to its original period $T$, the new period is在 $g$ 不变的条件下，单摆的摆长增大为原来的 $4$ 倍。与原周期 $T$ 相比，新周期为
A $0.40~\mathrm{kg}$ block oscillates on a horizontal spring of force constant $k = 100~\mathrm{N/m}$. The frequency of oscillation is closest to一个 $0.40~\mathrm{kg}$ 的滑块在弹簧常数 $k = 100~\mathrm{N/m}$ 的水平弹簧上振动。振动频率最接近
A block-spring system in SHM has amplitude $A$ and total mechanical energy $E$. When the block is at $x = A/2$, the fraction of $E$ that is kinetic is一个弹簧质量系统做简谐运动，振幅为 $A$，总机械能为 $E$。当滑块位于 $x = A/2$ 时，$E$ 中动能所占的比例为
A uniform rod of mass $M$ and length $L$ swings with small amplitude about a frictionless pivot at one end. Its period is一根质量为 $M$、长度为 $L$ 的均匀杆绕一端的无摩擦轴以小振幅摆动。其周期为
A particle in SHM is described by $x(t) = A\cos(\omega t + \phi)$. At $t = 0$ the particle is at $x = 0$ and moving in the $+x$ direction. The phase constant $\phi$ is一个做简谐运动的质点，其位置为 $x(t) = A\cos(\omega t + \phi)$。在 $t = 0$ 时，质点位于 $x = 0$ 且向 $+x$ 方向运动。初相位 $\phi$ 为
A block oscillates in SHM on a horizontal spring with amplitude $A$ and angular frequency $\omega$. Its speed as it passes through the equilibrium position $x = 0$ is一个滑块在水平弹簧上以振幅 $A$、角频率 $\omega$ 做简谐运动。其经过平衡位置 $x = 0$ 时的速度为
A simple pendulum has period $T_\mathrm{E}$ on Earth, where the gravitational field strength is $g$. The same pendulum is taken to the Moon, where the gravitational field strength is $g/6$. Its new period $T_\mathrm{M}$ is一个单摆在地球上的周期为 $T_\mathrm{E}$，地球重力加速度为 $g$。将该单摆移至月球，月球重力加速度为 $g/6$。新周期 $T_\mathrm{M}$ 为
A block oscillates on a horizontal spring in SHM with amplitude $A$. The kinetic and elastic potential energies are equal at the position一个滑块在水平弹簧上以振幅 $A$ 做简谐运动。动能等于弹性势能的位置为
A uniform rod of length $L = 1.5~\mathrm{m}$ swings as a physical pendulum about a frictionless pivot at one end. Take $g = 9.8~\mathrm{m/s^2}$. Its small-amplitude period is closest to一根长 $L = 1.5~\mathrm{m}$ 的均匀杆绕一端无摩擦轴做实体摆运动。取 $g = 9.8~\mathrm{m/s^2}$，其小振幅周期最接近
A block in SHM on a horizontal spring has amplitude $A$ and angular frequency $\omega$. The ratio of its speed at $x = A/2$ to its maximum speed is一个在水平弹簧上做简谐运动的滑块，振幅为 $A$，角频率为 $\omega$。其在 $x = A/2$ 处的速度与最大速度之比为
A block of mass $m$ on a horizontal spring of force constant $k$ oscillates in SHM with amplitude $A$ and angular frequency $\omega$. Which expression(s) below correctly give the total mechanical energy of the system?一个质量为 $m$ 的滑块在弹簧常数 $k$ 的水平弹簧上以振幅 $A$、角频率 $\omega$ 做简谐运动。下列哪个（些）表达式正确给出了系统的总机械能？
I. $\dfrac{1}{2}kA^2$ II. $\dfrac{1}{2}m\omega^2 A^2$
A block of mass $m$ on a horizontal frictionless surface is attached to a spring of force constant $k$. The block's equation of motion takes the form $m\,\dfrac{d^2x}{dt^2} + kx = 0$. The angular frequency of oscillation is一个质量为 $m$ 的滑块在水平无摩擦面上与弹簧常数 $k$ 的弹簧相连。滑块的运动方程为 $m\,\dfrac{d^2x}{dt^2} + kx = 0$。振动的角频率为
Show all work in the space provided. Partial credit is awarded for correct setup, units, and reasoning. Use $g = 9.8~\mathrm{m/s^2}$ unless otherwise stated.请在所提供的空白处展示所有解题过程。正确的解题步骤、单位及推理可获得部分分数。除非另有说明，使用 $g = 9.8~\mathrm{m/s^2}$。
A $0.40~\mathrm{kg}$ block, attached to a spring of force constant $k = 100~\mathrm{N/m}$, oscillates on a horizontal frictionless surface with amplitude $A = 0.10~\mathrm{m}$.一个 $0.40~\mathrm{kg}$ 的滑块与弹簧常数 $k = 100~\mathrm{N/m}$ 的弹簧相连，在水平无摩擦面上以振幅 $A = 0.10~\mathrm{m}$ 振动。
A particle moves in SHM along the $x$-axis according to $x(t) = 0.20\cos\!\left(4t + \dfrac{\pi}{3}\right)~\mathrm{m}$, where $t$ is in seconds.一个质点沿 $x$ 轴做简谐运动，位置方程为 $x(t) = 0.20\cos\!\left(4t + \dfrac{\pi}{3}\right)~\mathrm{m}$，其中 $t$ 的单位为秒。
A uniform rod of mass $M = 0.50~\mathrm{kg}$ and length $L = 1.20~\mathrm{m}$ is pivoted at one end about a frictionless horizontal axis. The rod is held at $\theta_0 = 30^\circ$ from the downward vertical and released from rest.一根质量 $M = 0.50~\mathrm{kg}$、长度 $L = 1.20~\mathrm{m}$ 的均匀杆绕一端无摩擦水平轴转动。将杆从竖直向下方向偏转 $\theta_0 = 30^\circ$ 后由静止释放。
A block of mass $m = 0.30~\mathrm{kg}$ is attached to a light spring of force constant $k = 60~\mathrm{N/m}$ that hangs vertically. The block is allowed to come to rest at its new equilibrium position; from there, it is pulled down by an additional $A = 0.10~\mathrm{m}$ and released from rest.一个质量 $m = 0.30~\mathrm{kg}$ 的滑块连接在弹簧常数 $k = 60~\mathrm{N/m}$ 的轻弹簧下端，弹簧竖直悬挂。滑块在新平衡位置静止后，再向下拉 $A = 0.10~\mathrm{m}$ 后由静止释放。