Question

The displacement of a particle executing S.H.M. is given by $y=10\sin (6t+\pi /3)$ in metre and time in seconds. The initial displacement and velocity of the particle are respectively :

• A. $25m$ and $5\sqrt{3}m/s$
• B. $15m$ and $5\sqrt{3}m/s$
• C. $15\sqrt{3}m$ and $30m/s$
• D. $10\sqrt{3}/2m$ and $30m/s$

Answer 1

The correct option is D $10\sqrt{3}/2m$ and $30m/s$

Initially $t=0;y=10sin\left(\frac{\pi }{3}\right)$

$=10\times \frac{\sqrt{3}}{2}=10\frac{\sqrt{3}}{2}m$

$v=\frac{dy}{dt}=60cos(6t+\frac{\pi }{3})$

At $t=0\Rightarrow 60\times cos\frac{\pi }{3}=30m/s$