Physics 9702 · AS & A Level · Energy in simple harmonic motion
Energy in simple harmonic motion — practice question
A simple pendulum is made up of a metal sphere hanging from a fixed point by a thread, as shown in Fig. 3.1. The sphere has mass $94.0\,\text{g}$ and is pulled sideways by a horizontal distance of $12.7\,\text{cm}$. Its centre of gravity rises vertically by $0.90\,\text{cm}$. The sphere is then released, so it oscillates. The sphere may be taken to oscillate with simple harmonic motion.
(a)[2]
State what simple harmonic motion means.
(b(i))[1]
State the kinetic energy of the sphere when the sphere comes back to the displaced position shown in Fig. 3.1.
(b(ii))[2]
Calculate the total energy $E_T$ of the oscillations.
(b(iii))[2]
Use your answer in (ii) to show that the angular frequency $\omega$ of the pendulum’s oscillations is $3.3\,\text{rad s}^{-1}$.
(c)[3]
The period $T$ of the pendulum’s oscillation is given by $T = 2\pi\sqrt{\frac{L}{g}}$, where $g$ is the acceleration of free fall and $L$ is the length of the pendulum. Use the data from (b) to determine $L$.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “acceleration varies in proportion to displacement” …