First slide

Simple harmonic motion

Question

A body executing simple harmonic motion has a maximum acceleration equal to $24 metres / \sec^{2}$ and maximum velocity equal to $16 metres / \sec$ . The amplitude of the simple harmonic motion is

Moderate

A

$\frac{32}{3} metres$
B

$\frac{3}{32} metres$
C

$\frac{1024}{9} metres$
D

$\frac{64}{9} metres$

Solution

Maximum velocity $= aω$ = 16
Maximum acceleration $= ω^{2} a = 24$
$\Rightarrow a = \frac{{(aω)}^{2}}{ω^{2} a} = \frac{16 \times 16}{24} = \frac{32}{3} m$

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