Q. An instantaneous displacement of a simple harmonic oscillator is $x = a\ cos(\omega t\ \pi/4).$ Its speed will be maximum at time
A) $\pi/4\omega$
B) $\pi/2\omega$
C) $\pi/\omega$
D) $2\pi/\omega$
Explanation
(a) Velocity, $v = \frac{dx}{dt} = - A\omega\sin{(\omega t + \pi/4)}$
Velocity will be maximum, when
$\omega t + \pi/4 = \pi/2$
or $\omega t = \pi/2 - \pi/4 = \pi/4\ \ \ \ or\ \ \ t = \pi/4\omega$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.