Paper 3 Oscillations and SHM Drills

Q1 Spring-mass oscillator

A mass $m=0.250\mathrm{kg}$ is attached to a horizontal spring of force constant $64.0\mathrm{N}{\mathrm{m}}^{-1}$. The mass is displaced $0.045\mathrm{m}$ from equilibrium and released from rest. Friction is negligible.

1. Show that the motion is SHM. [3]
2. Calculate the angular frequency and period. [3]
3. Calculate the maximum speed. [2]
4. Calculate the total mechanical energy. [2]
5. Explain the energy changes from maximum displacement to equilibrium. [2]

Q2 Pendulum and approximation

A simple pendulum of length $0.720\mathrm{m}$ performs small oscillations.

1. Calculate its period. [2]
2. Explain why the period is independent of bob mass in the ideal model. [2]
3. State two assumptions behind the simple-pendulum formula. [2]
4. The amplitude is made much larger. Explain why the small-angle formula becomes less reliable. [2]
5. Describe a practical method to reduce percentage uncertainty in the measured period. [2]