Physics - SHM Question with Solution | TestHub

The maximum acceleration in a simple harmonic motion is given by $a_{\text{max}}=A{\omega }^2$.

Given ${\omega }_1=300\text{ rad/s}$, ${\omega }_2=3000\text{ rad/s}$ and $A_1=A_2=A$.

The ratio of their maximum accelerations is

$\frac{a_{\text{max}1}}{a_{\text{max}2}}=\frac{A{\omega }_1^2}{A{\omega }_2^2}={\left(\frac{{\omega }_1}{{\omega }_2}\right)}^2$

$\frac{a_{\text{max}1}}{a_{\text{max}2}}={\left(\frac{300}{3000}\right)}^2={\left(\frac{1}{10}\right)}^2=\frac{1}{10^2}$

The ratio is $1:10^2$.

Answer: $1:10^2$