Question

Two simple harmonic motions of angular frequency $ 100 $ and $ 1000\, rad\, s^{-1} $ 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 $

Answer 1

Answer: (B)

Acceleration of simple harmonic motion is
$a_{\max }=-\omega^{2} A$
or $\frac{\left(a_{\max }\right)_{1}}{\left(a_{\max }\right)_{2}}=\frac{\omega_{1}^{2}}{\omega_{2}^{2}}$
(as $A$ remains same)
or $\frac{\left(a_{\max }\right)_{1}}{\left(a_{\max }\right)_{2}}=\frac{(100)^{2}}{(1000)^{2}}=\left(\frac{1}{10}\right)^{2}$
$=1: 10^{2}$