Question

The total vibrational energy of a particle in $\text{SHM}$ is $E$. Its kinetic energy at half the amplitude from mean position will be :

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

Answer 1

The correct option is D $3E/4$

Total vibrational energy$\left(E\right)$,
$E=\frac{1}{2}m{\omega }^2{A}^2$
$KE=\frac{1}{2}m{\omega }^2(A^2-x^2)$
$\Rightarrow KE=\frac{1}{2}m{\omega }^2(A^2-\frac{A^2}{4})$
$(\because x=A/2)$
$\Rightarrow KE=\frac{3}{4}\left(\frac{1}{2}m{\omega }^2{A}^2\right)=\frac{3E}{4}$
Hence, option $\left(d\right)$ is the correct answer.