📚 Describing Oscillations | 描述振动
Oscillations are among the most common types of motion observed in nature and engineering. A child on a swing, a vibrating guitar string, the alternating current in an electrical circuit, and even the beating of a heart all involve periodic back-and-forth movement about an equilibrium position. In A-Level physics, we describe oscillations quantitatively using key terms such as displacement, amplitude, period, frequency, and phase, and we classify a special type of oscillation called simple harmonic motion (SHM). Understanding how displacement, velocity, acceleration and energy vary during SHM is fundamental, as is the behaviour of real oscillators under damping and external forcing.
振动是自然界和工程中最常见的运动形式之一。荡秋千的孩子、振动的吉他弦、电路中的交流电、甚至心脏的跳动，都涉及围绕平衡位置的周期性往复运动。在A-Level物理中，我们使用位移、振幅、周期、频率和相位等关键术语定量描述振动，并特别将一类振动归类为简谐运动（SHM）。理解SHM过程中位移、速度、加速度和能量的变化规律，以及实际振动系统在阻尼和外力驱动下的行为，是本章的基础。
1. What is an Oscillation? | 什么是振动？
An oscillation is a motion that repeats itself at regular time intervals. The moving body passes through a central equilibrium position and reaches extreme points on either side. If undisturbed, ideal oscillations can continue forever, but real systems always lose energy to the surroundings due to friction or air resistance, eventually coming to rest.
振动是一种以固定时间间隔重复的运动。运动物体通过中心平衡位置，并到达两侧的极限点。理想情况下，无扰动的振动可以永远持续，但真实系统总会由于摩擦或空气阻力向周围环境耗散能量，最终停止。
Common examples include a mass on a spring, a simple pendulum swinging with small amplitude, and a tuning fork after being struck. Electrical oscillations, such as those in an LC circuit, also exhibit analogous behaviour.
常见的例子包括弹簧上的物块、小角度摆动的单摆以及被敲击后的音叉。LC电路中的电振荡也表现出类似的行为。
2. Simple Harmonic Motion (SHM) | 简谐运动
SHM is a mathematical model for a particular kind of periodic motion. An object moves with simple harmonic motion if its acceleration is directly proportional to its displacement from a fixed equilibrium position and is always directed towards that position. In equation form:
简谐运动是描述一类特定周期运动的数学模型。如果一个物体的加速度与其相对于固定平衡位置的位移成正比，且方向总是指向该平衡位置，则该物体做简谐运动。用方程表示为：
a = –ω² x
The negative sign indicates that acceleration and displacement are always in opposite directions. The constant ω is the angular frequency of the motion, measured in rad s⁻¹. This relationship is often called the defining equation of SHM.
负号表示加速度与位移方向总是相反。常数ω是振动的角频率，单位为rad s⁻¹。这一关系常被称为简谐运动的定义方程。
An equivalent differential equation is d²x/dt² = –ω² x. Systems that obey this equation, such as a mass–spring system where the restoring force obeys Hooke’s law (F = – M. For a simple pendulum swinging with small angles, the motion is also approximately SHM.
与之等价的微分方程为 d²x/dt² = –ω² x。遵循该方程的系统，例如回复力遵循胡克定律（F = –kx）的弹簧–质量系统，做简谐运动。对于小角度摆动的单摆，其运动也近似为简谐运动。
3. Defining Terms: Amplitude, Period, Frequency | 定义术语：振幅、周期、频率
To describe oscillations we use three basic quantities. The amplitude (A or x₀) is the maximum displacement from the equilibrium position. It is always a positive value and indicates the energy stored in the oscillator.
为描述振动，我们使用三个基本物理量。振幅（A 或 x₀）是偏离平衡位置的最大位移，总为正值，并反映振子储存的能量。
The period (T) is the time taken for one complete oscillation – number of complete oscillations per unit time and is measured in hertz (Hz), where 1 Hz =
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