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
$=\frac{\frac{1}{2}m{\omega }^2{y}^2}{\frac{1}{2}m{\omega }^2{a}^2}$
$=\frac{y^2}{a^2}=\frac{{\left(\frac{1}{4}a\right)}^2}{a^2}$
$\left(\text{ As }y=\frac{1}{4}a\right)$
$=\frac{1}{16}$