Question

The potential energy of particle following S.H.M at mean position is $6\text{Joules}$ and kinetic energy of particle at $X=\frac{A}{\sqrt{2}}$ is $8\text{Joules}$, find energy of oscillation.

• A. $14\text{J}$
• B. $10\text{J}$
• C. $22\text{J}$
• D. $30\text{J}$

Answer 1

The correct option is C $22\text{J}$

At $X=\frac{A}{\sqrt{2}}$
$V=\omega \sqrt{A^2-A^2/2}=\omega \frac{A}{\sqrt{2}}$
$\frac{1}{2}m{V}^2=8$
$\frac{1}{2}\frac{m{\omega }^2{A}^2}{2}=8$
$\frac{1}{2}m{\omega }^2{A}^2=16$
$K{E}_{max}=16$
$P{E}_{min}=6$
Total Energy $=KE+PE=16+6=22\text{Joule}$