Physics 9702 · AS & A Level · Simple harmonic oscillations

Simple harmonic oscillations — practice question

To illustrate simple harmonic motion, a student connects a trolley to two identical stretched springs, as shown in Fig. 3.1. The trolley has mass $m$ of $810\,\text{g}$. It is pulled along the line of the two springs and then let go. Its resulting acceleration $a$ is described by the expression $a = -\frac{2kx}{m}$ where the spring constant $k$ for each spring is $64\,\text{N m}^{-1}$ and $x$ represents the trolley’s displacement.
(a)[3]

Show that the trolley’s oscillation frequency is $2.0\,\text{Hz}$.

(b)[2]

The trolley’s maximum displacement is $1.6\,\text{cm}$. Calculate its maximum speed.

(c)[2]

The trolley’s mass is increased, while its initial displacement stays the same. Suggest what change, if any, occurs to the frequency and to the maximum speed of the trolley’s oscillations.

Worked solution & mark scheme

This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: Substitution of $\dfrac{2k}{m}=\omega^2$

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