2023HSCShort answer

Q11 (e)

2 marks

Question

A particle moves in simple harmonic motion described by $\ddot x=-9(x-4)$ . Find the period and the central point of motion.

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Solution

Criteria	Marks
Provides correct period and central point of motion	2
Provides correct period or centre, or equivalent merit	1

Sample answer:

$\ddot x=-3^2(x-4)$
$\therefore n=3\text{ and }c=4$
$\therefore T=\frac{2\pi}{n}=\frac{2\pi}{3}$
$\therefore\text{ Period}=\frac{2\pi}{3}\text{ and centre is }x=4$

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Syllabus alignment

Mechanics

Simple harmonic motionDerive and interpret displacement, velocity and acceleration models for simple harmonic motion.

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