Question

The potential energy of a simple harmonic oscillator when the particle is half way to its end point is: (where E is the total energy)

• A. $\frac{2}{3}E$
• B. $\frac{1}{8}E$
• C. $\frac{1}{4}E$
• D. $\frac{1}{2}E$

Answer 1

The correct option is C $\frac{1}{4}E$

Potential energy of simple harmonic oscillator
$=\frac{1}{2}m{\omega }^2{y}^2$
For $y=\frac{a}{2},PE=\frac{1}{2}m{\omega }^2\frac{a^2}{4}$
$\Rightarrow PE=\frac{1}{4}\left(\frac{1}{2}m{\omega }^2{a}^2\right)=\frac{E}{4}$
Hence, the correct answer is option(c).