Simple Harmonic Motion — A/L Physics

What must I remember about Simple Harmonic Motion?

• SHM Definition: Periodic motion where acceleration is directly proportional to displacement from a fixed equilibrium position and always directed toward that equilibrium position: a = -ω² x.
• Kinematic Equations of SHM: Displacement x = A sin(ωt + φ) or A cos(ωt); Velocity v = dx/dt = ± ω √(A² - x²); Maximum velocity v_max = ω A (at equilibrium x = 0); Maximum acceleration a_max = ω² A (at extremes x = ±A).
• Energy in SHM: Kinetic Energy KE = (1/2)m v² = (1/2)m ω² (A² - x²); Potential Energy PE = (1/2)m ω² x²; Total Mechanical Energy E_total = KE + PE = (1/2)m ω² A² = Constant.
• Standard SHM Oscillators: Simple Pendulum: Period T = 2π √(L/g) (for small amplitude θ < 10°); Mass-Spring System: T = 2π √(m/k).

Test yourself (1 minute)

1. Small Angle Approximation for Pendulum

   Period T = 2π √(L/g) is valid strictly for small oscillations where sin θ ≈ θ in radians (amplitude < 10°); for large angles, period increases.

2. Spring Combinations

   Two springs of stiffness k1 and k2: In Parallel: k_eq = k1 + k2; In Series: 1/k_eq = 1/k1 + 1/k2.

3. Phase Difference in SHM

   Velocity leads displacement by π/2 radians (90°); Acceleration leads displacement by π radians (180°).

Practise Simple Harmonic Motion questions today

Source: NIE G.C.E. (A/L) Physics Resource Book - Unit 3: Oscillations & Waves

What comes next?

Next in the syllabus

Where does Simple Harmonic Motion fit in the syllabus?

Unit 3.1 · Year 1 · Term 2