Question

$\begin{array}{c}\text{A particle is executing SHM of period}4\text{s. Then the time taken by it to move from}\\ \text{extreme position to half the amplitude is}\end{array}$

• A. $\frac{1}{3}s$
• B. $\frac{2}{3}s$
• C. $\frac{3}{4}s$
• D. $\frac{4}{3}s$

Answer 1

The correct option is B $\frac{2}{3}s$

$\begin{array}{c}x=A\cos wt\\ \Rightarrow \frac{A}{2}=A\cos wt\\ \Rightarrow wt=\frac{\pi }{3}\\ \Rightarrow t=\frac{\pi }{3\times w}\\ =\frac{\pi T}{3\times 2\pi }=\frac{T}{6}=\frac{4}{6}=\frac{2}{3}s\end{array}$

Hence,

option $\left(B\right)$ is correct answer.