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

The correct option is C Kinetic energy is maximum, potential energy is minimum

In $S.H.M$, kinetic energy of particle at any point $P$ is
Kinetic energy = $\frac{1}{2}m{\omega }^2(a^2-x^2)$
Potential energy = $\left(\frac{1}{2}m{\omega }^2{x}^2\right)$
where $a$ is amplitude of particle and $x$ is the distance from mean position.
So, at mean position, $x=0$
$K.E.=\frac{1}{2}m{\omega }^2{a}^2$ (maximum)
$P.E.=0$