Physics 9702 · AS & A Level · Simple harmonic oscillations
Simple harmonic oscillations — practice question
A pendulum is formed by a bob (tiny metal sphere) hanging from one end of a string, with the other end fixed at a point. The bob makes small oscillations about its equilibrium position, as shown in Fig. 4.1. The pendulum length $L$, measured from the fixed point to the centre of the bob, is $1.24\,\text{m}$. The acceleration $a$ of the bob changes with its displacement $x$ from equilibrium as shown in Fig. 4.2.
(a)[2]
State how Fig. 4.2 indicates that the pendulum's motion is simple harmonic.
(b(i))[2]
Use Fig. 4.2 to work out the angular frequency $\omega$ of the oscillations.
(b(ii))[2]
The angular frequency $\omega$ is linked to the pendulum length $L$ by $\omega = \sqrt{\frac{k}{L}}$, where $k$ is a constant. Use your answer in (b)(i) to find $k$. Include a unit with your response.
(c)[2]
While the pendulum is oscillating, the string length is increased so that the total energy of the oscillations stays constant. Suggest and explain the qualitative effect of this change on the amplitude of the oscillations.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “A straight line through the origin indicates $a \propto x$” …