Physics 9702 · AS & A Level · Simple harmonic oscillations

Simple harmonic oscillations — practice question

An oscillator causes a metal plate to vibrate up and down, as illustrated in Fig. 2.1. Sand is then scattered onto the plate. Fig. 2.2 shows how the sand’s acceleration $a$ varies with displacement $y$.
(a(i))[2]

Use Fig. 2.2 to demonstrate how it can be inferred that the sand is undergoing simple harmonic motion.

(a(ii))[2]

Calculate the oscillation frequency of the sand.

(b(i))[1]

The amplitude of oscillation of the plate is gradually increased beyond $8\,\text{mm}$. The frequency remains constant. At one amplitude, the sand is observed to lose contact with the plate. For the plate when the sand first loses contact with the plate, state the position of the plate.

(b(ii))[3]

Calculate the oscillation amplitude.

(b)

The amplitude of oscillation of the plate is gradually increased beyond $8\,\text{mm}$. The frequency remains constant. At a certain amplitude, the sand is observed to lose contact with the plate. For the plate when the sand first loses contact with the plate:

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