Question

The periodic time of a body executing simple harmonic motion is $3$ sec. After much interval form time $t=0$, its displacement will be half of its amplitude.

• A. $\frac{1}{8}sec$
• B. $\frac{1}{6}sec$
• C. $\frac{1}{4}sec$
• D. $\frac{1}{3}sec$

Answer 1

The correct option is C $\frac{1}{4}sec$

Given that, time period $T=3seconds$.

The equation for SHM is given by,

$y=Asin\omega t$ and $\omega =2\pi f=\frac{2\pi }{T}$

Let after time $t=t$, the displacement is half its amplitude,

$\Rightarrow \frac{A}{2}=Asin\left(\frac{2\pi }{3}t\right)$

$\Rightarrow sin\left(\frac{\pi }{6}\right)=sin\left(\frac{2\pi t}{3}\right)$

$\Rightarrow \frac{\pi }{6}=\frac{2\pi t}{3}$

or, $t=\frac{1}{4}sec$ is our required answer.