Oscillations and Waves: AS AQA Topic Test | 振荡与波：AS AQA 专题测试

📚 Oscillations and Waves: AS AQA Topic Test | 振荡与波：AS AQA 专题测试

This revision guide consolidates the core concepts of oscillations and waves for the OxfordAQA International AS Level Physics specification (Topic 5). Each section mirrors the examinable learning objectives and highlights common pitfalls in exam questions.

本复习指南系统梳理牛津AQA国际AS物理课程（第五主题）中振荡与波的核心概念。每个小节对应考纲要求的学习目标，并重点提示考试中常见的失分点。

1. Simple Harmonic Motion Fundamentals | 简谐运动基础

Simple harmonic motion (SHM) is defined as motion in which the acceleration of an object is directly proportional to its displacement from a fixed equilibrium position, and the acceleration is always directed towards that equilibrium position.

简谐运动（SHM）定义为：物体的加速度与其偏离固定平衡位置的位移成正比，且加速度方向始终指向平衡位置。

The defining equation of SHM can be written as:

简谐运动的定义方程可写为：

a = -ω²x

where a is acceleration in m s⁻², x is displacement from equilibrium in m, and ω (omega) is the angular frequency in rad s⁻¹. The negative sign indicates that acceleration is always opposite in direction to displacement.

其中 a 为加速度（单位 m s⁻²），x 为偏离平衡位置的位移（单位 m），ω（角频率）的单位为 rad s⁻¹。负号表示加速度方向始终与位移方向相反。

Key definitions include amplitude (A) – the maximum displacement from equilibrium; period (T) – the time for one complete oscillation; and frequency (f) – the number of oscillations per second. The relationship T = 1/f always holds.

关键定义包括：振幅（A）——离开平衡位置的最大位移；周期（T）——完成一次全振动所需的时间；频率（f）——每秒振动的次数。关系式 T = 1/f 始终成立。

For a mass-spring system, the period is given by T = 2π√(m/k), where m is the mass in kg and k is the spring constant in N m⁻¹. For a simple pendulum, T = 2π√(l/g), where l is the length and g is gravitational field strength.

对于弹簧振子系统，周期为 T = 2π√(m/k)，其中 m 为质量（kg），k 为劲度系数（N m⁻¹）。对于单摆，T = 2π√(l/g)，其中 l 为摆长，g 为重力场强度。

2. Equations and Graphs of SHM | 简谐运动的方程与图像

For an oscillator starting from maximum displacement, the displacement x at time t is given by x = A cos(ωt). If the oscillator starts from the equilibrium position, x = A sin(ωt) is used.

对于从最大位移开始计时的振子，t 时刻的位移为 x = A cos(ωt)。若从平衡位置开始计时，则使用 x = A sin(ωt)。

The velocity of an SHM oscillator is given by v = -Aω sin(ωt), and the maximum velocity v_max = Aω occurs as the object passes through the equilibrium position. The velocity-displacement relationship is v = ±ω√(A² – x²).

简谐运动振子的速度表达式为 v = -Aω sin(ωt)，最大速度 v_max = Aω 出现在经过平衡位置时。速度与位移的关系为 v = ±ω√(A² – x²)。

The acceleration is given by a = -Aω² cos(ωt) = -ω²x, confirming the defining equation of SHM. The maximum acceleration a_max = Aω² occurs at the extreme positions (maximum displacement).

加速度表达式为 a = -Aω² cos(ωt) = -ω²x，与定义方程一致。最大加速度 a_max = Aω² 出现在极端位置（最大位移处）。

When sketching SHM graphs, remember: the displacement-time graph is a cosine curve; the velocity-time graph is its negative sine (velocity leads displacement by 90° of phase); and the acceleration-time graph is an inverted displacement graph (acceleration is 180° out of phase with displacement).

绘制简谐运动图像时需注意：位移-时间图为余弦曲线；速度-时间图为其负正弦形式（速度相位领先位移 90°）；加速度-时间图是位移图的倒置形式（加速度与位移相位差 180

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