Physics 9702 · AS & A Level · Energy in simple harmonic motion

Energy in simple harmonic motion — practice question

A small object with mass $24\,\text{g}$ is resting on a platform. The platform is connected to an oscillator, as shown in Fig. 3.1, and the oscillator makes the platform move vertically up and down.
(a)[3]

The total energy of the object's oscillations is $2.2 \times 10^{-4}\,\text{J}$. Over one complete oscillation, the object covers a total distance of $14\,\text{mm}$. Calculate the angular frequency $\omega$ of the oscillations.

(b(i))[2]

The oscillator's frequency remains fixed, while the oscillation amplitude is increased gradually. Calculate the greatest amplitude of the oscillations so that the object stays in contact with the platform.

(b(ii))[2]

The amplitude of the oscillations is increased so that it is greater than the value in (b)(i). State and explain the point in an oscillation where the object first loses contact with the platform.

Worked solution & mark scheme

This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: $E = \frac12 m\omega^2 x_0^2$

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