Two simple harmonic motions of angular frequency 100 rad/s and 1000 rad/s have the same displacement…
Two simple harmonic motions of angular frequency 100 rad/s and 1000 rad/s have the same displacement amplitude. The ratio of their maximum acceleration is
$1: 10$
$1: 10^2$
$1: 10^3$
$1: 10^4$
Solution
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 $\frac{\left(a_{\max }\right)_1}{\left(a_{\max }\right)_2}=\frac{(100)^2}{(1000)^2}=\left(\frac{1}{10}\right)^2=1: 10^2$
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