Oscillations - Result Question 27

30. The potential energy of a simple harmonic oscillator when the particle is half way to its end point is

[2003]

(a) $\frac{1}{2} E$

(b) $\frac{2}{3} E$

(c) $\frac{1}{8} E$

(d) $\frac{1}{4} E$

where $E$ is the total energy

Show Answer

Answer:

Correct Answer: 30. (d)

Solution:

(d) $P . E .=\frac{1}{2} k x^{2}=E$

At half way

P.E. $=\frac{1}{2} k(\frac{x}{2})^{2}=\frac{\frac{1}{2} k x^{2}}{4}=\frac{E}{4}$