Question

The displacement of simple harmonic oscillator after $3$ seconds starting from its mean position is equal to half of its amplitude. The time period of harmonic motion is :

• A. 6 s
• B. 8 s
• C. 12 s
• D. 36 s

Answer 1

Answer: (D)

$X=A\sin \omega t\left(t=3,X=\frac{A}{2}\right)$
$\Rightarrow \frac{A}{2}=A\sin 3\omega$
$\Rightarrow \sin 3\omega =\frac{1}{2}$
$\Rightarrow 3\omega =\frac{\pi }{6}$
$\Rightarrow \omega =\frac{\pi }{18}=\frac{2\pi }{T}$
$\Rightarrow T=36s$