Question

A particle is executing linear simple harmonic motion. The fraction of the total energy that is potential, when its displacement is $ \frac{1}{4} $ of the amplitude is

• A. $ 1/16 $
• B. $ 1/8 $
• C. $ 1/2 $
• D. $ 1/4 $

Answer 1

Answer: (A)

For SHM, potential energy $=\frac{1}{2} m \omega^{2} y^{2}$
and total energy $=\frac{1}{2} m \omega^{2} a^{2}$
Therefore, fraction of potential energy
$=\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{1}{4} a\right)^{2}}{a^{2}} $
$\left(\text { As } y=\frac{1}{4} a\right) $
$=\frac{1}{16}$