Mechanics — Oscillations
Simple Harmonic Motion
SHM for small anglesT = 2π√(L/g)a = −ω²x | x = A cos(ωt)
Graph
Cosine wave — starts at +A, returns to +A each period T
Parameters
Length1 m
Amplitude15 °
Keep < 15° for accurate SHM
Mass0.5 kg
Does not affect period
Gravity9.81 m/s²
Moon=1.6 Earth=9.81 Jupiter=24.8
Calculated
Angular freq ω3.132 rad/s
Period T2.006 s
Frequency f0.498 Hz
Max velocity0.820 m/s
Max acceleration2.568 m/s²
Curriculum
WAECNECOIGCSESATJUPEB
📋 Teacher notes
- •Period T = 2π√(L/g) is INDEPENDENT of mass and amplitude (for small angles < 15°).
- •This independence of mass is why a pendulum makes a good clock — it keeps time regardless of the bob.
- •For large amplitudes, the period increases — the small-angle approximation (sinθ ≈ θ) breaks down.
- •On the Moon (g=1.6 m/s²), the same pendulum runs ~2.5× slower. The gravity slider demonstrates this.
- •A seconds pendulum (T=2s) has length L = g/π² ≈ 0.993m — almost exactly 1 metre.
✏️ Exercises