Paper 4 Oscillations and SHM Drills

Q1 Measuring spring oscillator period

A student measures the period $T$ of a mass-spring oscillator for different added masses $m$. The mass holder and part of the spring also contribute to the oscillating mass.

$m/\mathrm{kg}$	$T/\mathrm{s}$
0.050	0.150
0.100	0.187
0.150	0.217
0.200	0.245
0.250	0.268
0.300	0.292

1. Show that a graph of $T^2$ against $m$ should be linear. [2]
2. Calculate $T^2$ for each reading. [1]
3. Plot $T^2$ against $m$ and draw a best-fit straight line. [5]

4. Use the gradient to determine the spring constant. [3]
5. Use the intercept to estimate the effective additional oscillating mass. [2]
6. State two precautions for measuring $T$ reliably. [2]

Q2 Resonance experiment

A vibrator drives an oscillator at different frequencies. The steady-state amplitude is measured.

1. State how the resonant frequency is identified from the data. [1]
2. Explain why the system should be allowed to reach steady state before recording amplitude. [2]
3. State one effect of increasing damping on the graph. [1]
4. State one safety or apparatus precaution. [1]