ZIMSEC A Level · Physics · Form 5, Form 6
Simple harmonic motion
Acceleration is proportional to displacement and directed towards the equilibrium position: a = −ω²x.
- x = x₀ sin ωt; v = ±ω√(x₀² − x²); maximum speed ω x₀; maximum acceleration ω² x₀.
- Pendulum: T = 2π√(l/g); mass–spring: T = 2π√(m/k).
- Damping reduces amplitude; resonance occurs when the driving frequency equals the natural frequency.
Worked example: A simple pendulum has a length of 0.80 m. Find its period (g = 9.81 m s⁻²).
T = 2π√(0.80/9.81) = 2π × 0.2856 = 1.79 s
Waves
- v = fλ. Intensity ∝ amplitude². Transverse waves can be polarised; longitudinal waves cannot.
- Doppler effect for sound: observed frequency f′ = fv/(v ± vs) (minus when the source approaches).
Superposition
- Stationary waves form from two waves travelling in opposite directions: nodes (zero amplitude) and antinodes; distance between nodes = λ/2.
- Diffraction is greatest when the gap is similar to the wavelength.
- Two-source interference: fringe spacing x = λD/a.
- Diffraction grating: d sin θ = nλ.
Worked example: Light of wavelength 600 nm falls on a grating with 300 lines per mm. Find the angle of the first-order maximum.
d = 1/300 000 m = 3.33 × 10⁻⁶ m; sin θ = 600 × 10⁻⁹ ÷ 3.33 × 10⁻⁶ = 0.180 → θ = 10.4°
Exam tip: Convert lines per mm into slit spacing d in metres before using d sin θ = nλ.
Check yourself
- A wave has frequency 50 Hz and wavelength 6.8 m. Find its speed.
- What is the distance between adjacent nodes in a stationary wave?
- State the condition for resonance.
Show answers
- 340 m s⁻¹
- Half a wavelength (λ/2).
- The driving frequency equals the natural frequency of the system.
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