Q. The instantaneous displacement of a simple harmonic oscillator is given by$= a\cos\left\lbrack \omega t + \frac{\pi}{4} \right\rbrack$. Its speed will be maximum at the time
A) $\frac{2\pi}{\omega}$
B) $\frac{\omega}{2\pi}$
C) $\frac{\omega}{\pi}$
D) $\frac{\pi}{4\omega}$
Explanation
(d) Speed is maximum when y=a
$\therefore\ \ \ a = a\cos\left( \omega t + \frac{\pi}{4} \right)$
$\Longrightarrow \ \ \cos{\left( \omega t + \frac{\pi}{4} \right) = 1}$
$\Longrightarrow \omega t + \frac{\pi}{4} = 0 \Longrightarrow t = - \frac{\pi}{4\omega}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.