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

Answer: (D)

1 : $10^2$

Answer 2

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