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 direction of the two springs and then let go. The resulting acceleration $a$ of the trolley is described by $a = -\frac{2kx}{m}$, where the spring constant $k$ for each spring is $64\,\text{N m}^{-1}$ and $x$ is the trolley’s displacement.
(a)[3]

Demonstrate that the trolley oscillates with a frequency of $2.0\,\text{Hz}$.

(b)[2]

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

(c)[2]

The mass of the trolley is increased. The initial displacement of the trolley stays the same. Suggest the change, if any, in the frequency and in 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: $\frac{2k}{m}=\omega^2$

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