Physics 9702 · AS & A Level · Simple harmonic oscillations

Simple harmonic oscillations — practice question

A block is attached to a spring and hangs freely. It oscillates vertically in simple harmonic motion. The block's velocity $v$ varies with time $t$ according to $v = 0.56\cos 16t$, where $v$ is in $\text{m s}^{-1}$ and $t$ is in $\text{s}$.
(a)[2]

State the meaning of simple harmonic motion.

(b(i))[1]

Calculate the period of the oscillation.

(b(ii))[2]

Determine the oscillation amplitude $x_0$.

(b(iii))[1]

Use your result in (b)(ii) to determine an equation for $v$ in terms of the block's displacement $x$, where $v$ is in $\text{m s}^{-1}$ and $x$ is in $\text{m}$.

(b(iv))[3]

On Fig. 5.1, sketch how $v$ varies with $x$.

(iv)[3]

On Fig. 5.1, sketch the graph of $v$ against $x$.

Worked solution & mark scheme

This 12-mark question has a full step-by-step worked solution and mark scheme. One marking point: acceleration varies in direct proportion to displacement

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