Question

The kinetic energy and potential energy of a particle executing SHM will be equal when displacement ($amplitude=a$) is

• A. $a\sqrt{2/3}$
• B. $a/2$
• C. $a/\sqrt{2}$
• D. $a\sqrt{2}$

Answer 1

The correct option is C $a/\sqrt{2}$

$K.E.=P.E.\Rightarrow \frac{1}{2}m{\omega }^2(a^2-x^2)=\frac{1}{2}m{\omega }^2{x}^2\Rightarrow a^2-x^2=x^2\Rightarrow 2x^2=a^2\Rightarrow x=a/\sqrt{2}$