A body executing simple harmonic motion has a maximum acceleratio… - Vidyadip

MCQ

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

✓
$\frac{32}{3}$ metres
B
$\frac{3}{32}$ metres
C
$\frac{1024}{9}$ metres
D
$\frac{64}{9}$ metres

✓

Answer

Correct option: A.

$\frac{32}{3}$ metres

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

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