Question

The time period of oscillation of a S.H.O. is $\frac{\pi }{2}s$. Its acceleration at a phase angle $\frac{\pi }{3}$ rad from extreme position is $2m/s^2$, what is its velocity at a displacement equals to half of its amplitude from mean position?

• A. $0.707m/s$
• B. $0.866m/s$
• C. $\sqrt{2}m/s$
• D. $\sqrt{3}m/s$

Answer 1

The correct option is B $0.866m/s$

$a={\omega }^{2}x$
$x=Acos\frac{\pi }{3}$
$\omega =\frac{2\pi }{T}$
$T=\frac{\pi }{2}$
$\omega =4$
$2=(4T^2\times A\times \frac{1}{2})$
$A=\frac{1}{4}$
$V=\omega \times \sqrt{(A{)}^2-x^2}$
$x=\frac{A}{2}$
$V=\omega A\times \frac{\sqrt{3}}{2}$
$V=0.866m/sec$