Question

The displacement of an object attached to a spring and executing simple harmonic motion is given by $x=2\times {10}^{-2}cos\pi$t metres. The time at which the maximum speed first occurs is -

• A. $0.5s$
• B. $0.75s$
• C. $0.125s$
• D. $0.25s$

Answer 1

Answer: (A)

$0.5s$

Given, displacement $x=2\times {10}^{-2}\cos \pi t$

The magnitude of velocity , $v=|\frac{dx}{dt}|=2\pi \times {10}^{-2}\sin \pi t$

So, the velocity will be maximum when $\sin \pi t=1$ where $\pi t=\frac{\pi }{2},\frac{3\pi }{2},..$

So for first maximum, $\pi t=\frac{\pi }{2}$ or $t=0.5s$