Question

What should be the displacement of a simple pendulum whose amplitude is $A$ when its potential energy is $1/4th$ of the total energy ?

• A. $A/6$
• B. $A/2$
• C. $A/4$
• D. $A/3$

Answer 1

The correct option is B $A/2$

$PE=\frac{1}{2}m{\omega }^2{x}^2$
$TE=\frac{1}{2}m{\omega }^2{A}^2$
$PE=\frac{TE}{4}$
$\frac{1}{2}m{\omega }^2{x}^2=\frac{1}{2}m{\omega }^2{A}^2\times \frac{1}{2}$
$x=\frac{A}{2}$