Question

A particle is performing $SHM$ of amplitude $A$ and time period $T$. Find the time taken by the particle to go from $x=0$ to $x=\frac{A}{2}$.

• A. $\frac{T}{4}$
• B. $\frac{T}{8}$
• C. $\frac{T}{12}$
• D. $\frac{T}{16}$

Answer 1

The correct option is C $\frac{T}{12}$

let equation of $SHM$ be, $x=A\sin \omega t$

at $x=0,t=0$

at $x=\frac{A}{2}\Rightarrow \frac{A}{2}=A\sin \omega t$

$\Rightarrow \sin \omega t=\frac{1}{2}$

$\therefore \omega t=\frac{\pi }{6}$

$\frac{2\pi }{T}t=\frac{\pi }{6}\Rightarrow t=\frac{T}{12}$

So, time taken is $\frac{T}{12}$

Hence, $\left(C\right)$ is the correct answer.

Why this question? tip : This question deals with the initial phase of $SHM$ and finding its equation to find time taken from mean position to $\frac{A}{2}.$