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

Answer 1

Answer: (B)

$\frac{1}{4}E$

Answer 2

$\frac{U}{E} = \frac{\frac{1}{2}m\omega^{2}y^{2}}{\frac{1}{2}m\omega^{2}a^{2}} = \frac{y^{2}}{a^{2}} = \frac{\left( \frac{a}{2} \right)^{2}}{a^{2}} = \frac{1}{4}$ ⇒ $U = \frac{E}{4}$