Physics - SHM Question with Solution | TestHub

Kinetic energy in SHM,

$K=\frac{1}{2}m{\omega }^2\left(a^2-x^2\right)$

Potential energy in SHM,

$U=\frac{1}{2}m{\omega }^2{x}^2$

Given that,$K=3U$

$\Rightarrow \frac{1}{2}m{\omega }^2\left(a^2-x^2\right)=3\cdot \frac{1}{2}m{\omega }^2{x}^2$

$a^2-x^2=3x^2$

$a^2=4x^2$

$a=2x$

$2x=a$

$\frac{x}{a}=\frac{1}{2}$