State the meaning of resonance.
Fig. 4.1 shows a heavy pendulum and a light pendulum, both hanging from the same string. This string is fixed at each end to stationary points. Both pendulums have the same natural frequency. The heavy pendulum is made to oscillate perpendicular to the plane of the diagram. As it moves, it causes the light pendulum to oscillate. Fig. 4.2 shows how the displacements of the two pendulums vary with time $t$ over three oscillations.
The displacement $x$ of the light pendulum varies with $t$ according to $x = 0.25\sin 5.0\pi t$, where $x$ is measured in centimetres and $t$ in seconds. Calculate the period $T$ of the oscillations.
On Fig. 4.2, add labels to both axes with the correct scales. Use the space below for any extra working that you require.
Find the magnitude of the phase difference $\phi$ between the oscillations of the light and heavy pendulums. Include a unit in your answer.