📚 Year 13 WJEC Physics: Core Concepts Summary | Year 13 WJEC 物理：核心知识点梳理
The second year of WJEC A-level Physics (Year 13) consolidates and extends your understanding of key physical principles through two core units: Unit 3 – Oscillations and Nuclei, and Unit 4 – Fields and Options. This article provides a concise yet comprehensive overview of the essential topics, including simple harmonic motion, thermodynamics, nuclear physics, gravitational, electric and magnetic fields, electromagnetic induction, and capacitors, along with a brief look at the optional topics. Mastering these concepts is crucial for success in the final examinations and for building a solid foundation for further study in physics or engineering.
WJEC A-level 物理的第二年（Year 13）通过两个核心单元巩固和拓展你对关键物理原理的理解：单元三——振荡与原子核，以及单元四——场与选项。本文围绕简谐运动、热力学、核物理、引力场、电场、磁场、电磁感应和电容器等重要主题，提供简明而全面的知识点梳理，并简要介绍选项内容。掌握这些概念对在最终考试中取得好成绩以及为物理或工程的后续学习打下坚实基础至关重要。
1. Simple Harmonic Motion (SHM) | 简谐运动
ibrium and directed towards it: a is proportional to minus x. The defining equation is a = – angular frequency. Solutions include x = A cos(ωt) or x = A sin(ωt), with velocity v = ±ω√A² – x².
简谐运动是一种周期性运动，恢复力（及加速度）与位移成正比且方向相反：a 正比于 –x。定义方程为 a = –ω²x，ω 为角频率。解的形式为 x = A cos(ωt) 或 x = A sin(ωt)，速度 v = ±ω√A² – x²。
a = –ω²x
independent of amplitude for simple harmonic oscillators; for a mass-spring system T = 2π√m/k and for a simple pendulum T = 2π√l/g and potential, with total energy E = ½mω²A² remaining constant in the absence of damping.
周期 T = 2π/ω 与振幅无关；对于弹簧振子 T = 2π√m/k，对于单摆 T = 2π√l/g，均基于小角度近似。能量在动能和势能之间不断转换，总能量 E = ½mω²A² 在无阻尼时保持不变。
2. Damped and Forced Oscillations | 阻尼与受迫振荡
Damping reduces the amplitude over time due to resistive forces; light, critical and heavy damping describe different decay behaviours. Critical damping allows the fastest return to equilibrium without oscillation. Forced oscillations occur when an external periodic force drives the system; resonance happens when the driving frequency matches the natural frequency, producing a maximum amplitude and potentially causing catastrophic failures.
阻尼由于阻力使振幅随时间减小；轻阻尼、临界阻尼和过阻尼描述不同的衰减行为。临界阻尼使系统最快回到平衡位置且不振荡。受迫振荡发生时，外部周期性力驱动系统；当驱动频率等于固有频率时发生共振，振幅达到最大，可能造成灾难性破坏。
ω, where Δω is the bandwidth. High Q implies low damping and a sharp peak. Practical examples include vehicle suspension and oscillating bridges.
共振的尖锐程度用品质因数 Q = ω₀/Δω 表征，Δω 为带宽。高 Q 值表示低阻尼和尖锐的共振峰。实际例子包括车辆悬挂系统和摇摆的桥梁。
3. Thermal Physics and Ideal Gases | 热力学与理想气体
he average kinetic energy of particles; the Kelvin scale is used with absolute zero (0 K = – The kinetic theory model links macroscopic properties to microscopic behaviour: pV = ⅓N m⟨c²⟩.
温度是粒子平均动能的量度；使用开尔文温标，绝对零度为 0 K = –273.15 °C。理想气体状态方程为 pV = nRT，n 为摩尔数，R = 8.31 J mol⁻¹ K⁻¹。分子运动论将宏观量与微观行为联系起来：pV = ⅓N m⟨c²⟩。
pV = nRT
The average translational kinetic energy of a molecule is ½m⟨c²⟩ h W being work done ON the system. Adiabatic processes follow pV^γ = constant, where γ = Cp/Cv.
分子的平均平动动能为 ½m⟨c²⟩ = (3/2)kT，k 为玻尔兹曼常数。WJEC 使用的热力学第一定律通常为 ΔU = Q + W，其中 W 是对系统做的功。绝热过程满足 pV^γ = 常数，γ = Cp/Cv。
4. Nuclear Decay and Radioactivity | 核衰变与放射性
, beta (β⁻, β⁺) and gamma emission. Radioactive decay follows an exponential law: N = N₀ e–λt e λ is the decay constant. The half-life t½ = ln 2/λ remains constant for a given isotope.
原子核由质子和中子组成；强核力克服静电斥力。不稳定核通过 α、β⁻、β⁺ 和 γ 衰变。放射性衰变遵从指数规律：N = N₀ e–λt，λ 为衰变常数。半衰期 t½ = ln 2/λ 对特定同位素保持不变。
N = N₀ e–λt
Activity A = λN decays similarly. The decay constant is related to the mean life τ = 1/λ.
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