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 : $ 10^3 $
• B. 1 : $ 10^4 $
• C. 1 : $ 10 $
• D. 1 : $ 10^2$

Answer 1

The Correct Option is D

$ \omega_1 = 100 \, rad \, s^{ - 1} ; \, \omega_2 = 1000 \, rad \, s^{-1}$.
Maximum acceleration of (1) = - $ \omega_1^2 \, A $
Maximum acceleration of (2) = - $ \omega_2^2 \, A $
$ \therefore \frac{ accln \, (1) }{ accln \, (2) } = \frac{ \omega_1^2}{ \omega_2^2 } = \frac{(1 00)^2 }{ (1000)^2 } = \frac{1}{ 100}$
$a (1) : a (2) = 1 : 100$.