Q. Two simple harmonic motions of angular frequency 100 and 1000 rad/s have the same displacement amplitude. The ratio of their maximum acceleration is
A) 1:10
B) $1:10^{2}$
C) $1:10^{3}$
D) $1:10^{4}$
Explanation
(b) Acceleration of simple harmonic motion is
$a_{max\ } = - {\omega^{2}A}$
or $\frac{({a_{\max})}_{1}}{{(a_{\max})}_{2}} = \frac{\omega_{1}^{2}}{\omega_{2}^{2}}$ (as $A$ remains same)
or $\frac{({a_{\max})}_{1}}{{(a_{\max})}_{2}} = \frac{(100)^{2}}{(1000)^{2}} = \left( \frac{1}{10} \right)^{2} = 1:10^{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.