Question

In a simple harmonic oscillator, at the mean position:

• A. kinetic energy is minimum, potential energy is maximum
• B. both kinetic and potential energies are maximum
• C. kinetic energy is maximum, potential energy is minimum
• D. both kinetic and potential energies are minimum

Answer 1

Answer: (C)

Kinetic energy of particle of mass $m$ in SHM at any point is,
$=\frac{1}{2}m{\omega }^2\left(a^2-x^2\right)$
and potential energy $=\frac{1}{2}m{\omega }^2{x}^2$
where, $a$ is amplitude of particle and $x$ is the distance from mean position. So, at mean position, $x=0$
$KE=\frac{1}{2}m{\omega }^2{a}^2$ (maximum)
$PE=0$ (minimum)