Physics 9702 · AS & A Level · Simple harmonic oscillations
Simple harmonic oscillations — practice question
As shown in Fig. 4.1, a mass is suspended vertically from a fixed point by a spring. The mass is then displaced vertically and released. Its resulting oscillations are simple harmonic. Fig. 4.2 shows how the spring length $l$ changes with time $t$.
(a(i))[1]
From Fig. 4.2, state two values of $t$ when the mass is moving downwards at maximum speed.
(a(ii))[2]
Find the angular frequency $\omega$ for these oscillations.
(a(iii))[2]
Show that the mass has a maximum speed of $0.42\,\text{m s}^{-1}$.
(b)[3]
Using the information in Fig. 4.2 and part (a)(iii), sketch on the axes of Fig. 4.3 how the velocity of the mass varies with displacement $x$ from the equilibrium position.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “The two times are $0.225\,\text{s}$ and $0.525\,\text{s}$” …