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)

$1/16$

Answer 2

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