Question

The periodic time of a particle doing simple harmonic motion is $4$s. The time taken for it to go from its mean position to half the maximum displacement (amplitude) is.

• A. $2s$
• B. $1s$
• C. $\frac{2}{3}s$
• D. $\frac{1}{3}s$

Answer 1

The correct option is D $\frac{1}{3}s$

$y=A\sin \left(\frac{2\pi }{T}\right)t$
$\Rightarrow \frac{A}{2}=A\sin \left(\frac{2\pi }{4}\right)t$
$\Rightarrow \frac{\pi t}{2}=\frac{\pi }{6}$
$\Rightarrow t=\frac{1}{3}s$