Question

Two simple harmonic motions of angular frequency $100$ and $1000rad{s}^{-1}$ 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 $\frac{{\left(a_{\max }\right)}_1}{{\left(a_{\max }\right)}_2}=\frac{(100{)}^2}{(1000{)}^2}={\left(\frac{1}{10}\right)}^2$
$=1:10^2$