First slide

Simple hormonic motion

Question

The displacement of a particle executing SHM is given by y = 10 sin (3t + $\frac{\pi }{3}$ )m and ‘t’ is in seconds. The initial displacement and maximum velocity of the particle are respectively

Easy

A

$\large 5\sqrt 3$ m and 30m/sec
B

15m and $\large 15\sqrt 3$ m/sec
C

$\large 15\sqrt 3 \,m$ and 30 m/sec
D

$\large 20\sqrt 3 \,m$ and 30 m/sec

Solution

$\large y\, = \,10\sin \left( {3t + \frac{\pi }{3}} \right)m$
At t = 0, $\large y\, = \,10\sin \frac{\pi }{3}\,m\,\,\, = \,\,5\sqrt 3 m$
$\large V = \,\frac{{dy}}{{dt}}\, = \,30\cos \left( {3t + \frac{\pi }{3}} \right)$
$\large \therefore {V_{\max }}\, = \,30m/s$

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