Physics 9702 · AS & A Level · Simple harmonic oscillations

Simple harmonic oscillations — practice question

A block with mass $m$ vibrates vertically on a spring, as illustrated in Fig. 4.1. The block’s acceleration $a$ changes with displacement $x$ from equilibrium, as plotted in Fig. 4.2. The oscillation amplitude is $3Y$ and the greatest acceleration is $2A$.
(a)[2]

Explain how Fig. 4.2 indicates that the block’s oscillations are simple harmonic.

(b(i))[1]

Deduce an expression, using some or all of $m$, $A$ and $Y$, for the angular frequency $\omega$ of the oscillations.

(b(ii))[2]

Deduce an expression, using some or all of $m$, $A$ and $Y$, for the maximum speed $v_0$ of the oscillations.

(b(iii))[2]

Deduce an expression, using some or all of $m$, $A$ and $Y$, for the energy $E$ of the oscillations.

(c)[2]

The period is $0.75\,\text{s}$ and $3Y$ has the value $1.8\,\text{cm}$. Find an equation for $x$ in terms of time $t$, with $x$ measured in cm and $t$ measured in seconds.

Worked solution & mark scheme

This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: A straight line passing through the origin, so $a \propto x$

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