First slide

Applications of SHM

Question

The displacement of an object attached to a spring and executing simple harmonic motion is given by ${x=2×10}^{-2} cos(πt) meter$ . The time at which the maximum speed first occurs is

Moderate

A

0.5 seconds
B

1 second
C

1.5 seconds
D

2 seconds

Solution

Given displacement ${x=2×10}^{-2} cos(πt)$
velocity is obtained by differentiating above equation,
$v= \frac{dx}{dt} = - 2 \times 10^{- 2} πsin(πt)$
For the first time when ${v=v}_{max}$
$sinπt=1$
$sinπt=sin \frac{π}{2}$
$πt= \frac{π}{2}$
T=0.5 seconds.

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