Q. Starting from $y = A\sin{\omega t\ or\ y = A\cos{\omega t}}$
A) acceleration lags the displacement by a phase $\pi/4$
B) acceleration lags the displacement by a phase $\pi/2$
C) acceleration leads the displacement by a phase $\pi/2$
D) acceleration leads the displacement by a phase $\pi$
Explanation
(d) $y = a\sin{\omega t;v = \frac{dy}{dt} = a\omega}\cos{\omega t}$
$= a\omega\sin{(\omega t + \pi/2)}$
Acceleration $A = \frac{dv}{dt} = - \omega^{2}a\sin{\omega t}$
$= \omega^{2}a\sin{(\omega t + \pi)}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.