Question

The displacement of a body executing SHM is given by $x=Asin(2\pi t+\pi /3)$.The first time from $t=0$ when the velocity is maximum is

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

Answer 1

The correct option is A $0.33sec$

$x=Asin(2\pi t+\frac{\pi }{3})$
Velocity is maximum at mean position i.e. $x=0$
$\Rightarrow sin(2\pi t+\frac{\pi }{3})=0\Rightarrow (2\pi t+\frac{\pi }{3})=0,\pi ,2\pi ,3\pi ....$
if we take $(2\pi t+\frac{\pi }{3})=0$, time will come negative which is not possible. So we take $(2\pi t+\frac{\pi }{3})=\pi$
$\Rightarrow t=\frac{1}{3}s=0.33s$
for other solutions, we will get higher values of time. but Since it is asking for the first time after $t=0$, the required solution will be $t=0.33s$