Question

A particle executing a simple harmonic motion has a period of $6\,sec$. The time taken by the particle to move from the mean position to half the amplitude, starting from the mean position is.

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

Answer 1

Answer: (B)

Equation for simple harmonic motion
$y =a \,sin \left(\frac{2 \pi}{T}\right) t$
$\frac{a}{2} =a\,sin \left(\frac{2 \pi}{T}\right) t$
$\Rightarrow \frac{2 \pi}{T} t =\frac{\pi}{6}$
$ \left(\because y=\frac{a}{2}\right)$
$t=\frac{T}{12}=\frac{6}{12}=\frac{1}{2} s$