Question

The displacement of a body executing SHM is given by x = A sin (2$\pi t$ + $\frac{\pi }{3}$). The first time from t = 0 when the velocity is maximum is:

• A. 0.33 sec
• B. 0.16 sec
• C. 0.25 sec
• D. 0.5 sec

Answer 1

The correct option is A 0.33 sec

The displacement of a body executing SHM is given by:

$x=Asin(2\pi t+\pi /3)$

Velocity, $v=\frac{dx}{dt}=2\pi Acos(2\pi t+\pi /3)$

For maximum velocity,

$\frac{dv}{dt}=0$

$\Rightarrow -4{\pi }^{2}Asin(2\pi t+\pi /3)=0$

$\Rightarrow sin(2\pi t+\pi /3)=sin\left(n\pi \right)$

$\Rightarrow 2\pi t+\pi /3=n\pi$

for $n=1$

$\Rightarrow 2\pi t=\pi -\pi /3=\frac{2\pi }{3}$

$t=\frac{1}{3}=0.33sec$

The correct option is A.