In a simple harmonic oscillator, at the mean positionA. Kinetic energy is minimum, potential energy is maximumB. Both kinetic and potential energies are maximumC. Kinetic energy is maximum, potential energy is minimumD. Both kinetic and potential energies are minimum

In a simple harmonic oscillator, such as a mass attached to a spring, the motion oscillates back and forth around an equilibrium or mean position. At the mean position (the point of maximum displacement from the equilibrium), the velocity of the oscillator is maximum, and the displacement from the equilibrium is zero.

The kinetic energy (KE) of an object is given by the formula:

KE = (1/2) * m * v^2

Where:
KE = Kinetic Energy
m = mass of the object
v = velocity of the object

Since at the mean position, the velocity (v) is maximum (as it changes direction), the kinetic energy is also maximum.

The potential energy (PE) of a spring in a simple harmonic oscillator is given by:

PE = (1/2) * k * x^2

Where:
PE = Potential Energy
k = spring constant
x = displacement from the equilibrium position

At the mean position, the displacement (x) is zero, which means the potential energy is also minimum because there is no stretch or compression of the spring at that point.

So, the correct answer is:

C. Kinetic energy is maximum, potential energy is minimum.