Question

The ratio of displacement to amplitude, when the kinetic energy of a body executing SHM is thrice the potential energy is,

• A. $\frac{3}{2}$
• B. $\frac{4}{3}$
• C. $\frac{1}{2}$
• D. $\frac{2}{3}$

Answer 1

Answer: (C)

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, $K=3U$
$\Rightarrow \frac{1}{2}m{\omega }^2\left(a^2-x^2\right)=3\cdot \frac{1}{2}m{\omega }^2{x}^2$
$a^2-x^2=3x^2$
$a^2=4x^2$
$a=2x$
$2x=a$
$\frac{x}{a}=\frac{1}{2}$