Physics 9702 · AS & A Level · Simple harmonic oscillations
Simple harmonic oscillations — practice question
A pendulum is made from a bob (a small metal sphere) hung from the lower end of a length of string. The upper end of the string is fixed to a point. The bob makes small oscillations about its equilibrium position, as shown in Fig. 4.1. The length $L$ of the pendulum, taken 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 the equilibrium position, 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 find the angular frequency $\omega$ of the oscillations.
(b(ii))[2]
The angular frequency $\omega$ depends on the pendulum length $L$ according to $\omega = \sqrt{\frac{k}{L}}$, where $k$ is a constant. Use your answer in (b)(i) to determine $k$. Include a unit in your response.
(c)[2]
As the pendulum is oscillating, the string length is increased in such a way that the total energy of the oscillations stays constant. Suggest and explain qualitatively how this affects 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 shows $a \propto x$.” …