The total mechanical energy of a simple harmonic oscillator is
a. a minimum when it passes through the equilibrium point.
b. zero when it reaches the maximum displacement.
c. zero as it passes the equilibrium point.
d. constant.
e. a maximum when it passes through the equilibrium point.

An example of a simple harmonic oscillator is an object attached to a spring.

The body starts out in static equilibrium. There is no net force on it and it is not moving.

Let's pull it a few centimeters from its equilibrium spot and let go. We just did some work against the spring force in order to move the body and deform the spring. Whatever work we just did in deforming the spring becomes stored as the spring's potential energy. Now watch what happens.

The spring force acts as a restoring force, trying to move the body back to its cozy equilibrium spot with a force proportional to the body's displacement. Whatever work the spring does on the body in the process becomes the body's change in kinetic energy.

When the body reaches the equilibrium spot, the spring no longer exerts a force on it, but it doesn't stop there. The body's kinetic energy makes it overshoot the equilibrium spot. Beyond this spot we now have a spring force acting the opposite way, and the body has to do work against the spring force in order to keep displacing itself further. This work, just like the work we did with our own hands earlier, becomes stored as the spring's potential energy. Do you see where we're going with this?

At some point, the body drains itself of its kinetic energy, and now the spring, with its potential energy maxed out, starts doing work on the body to move it back to the equilibrium spot.

If we observed the body's kinetic energy and the spring's potential energy over time, they will reach their maximum values at different times. These quantities fluctuate in such a way that when the kinetic energy is 0, the potential energy is maxed out, and when the kinetic energy is maxed out, the potential energy is 0. Furthermore, at all points in time, the sum of the kinetic energy and the potential energy of the spring-mass system, which is its total mechanical energy, will remain constant over time.

Choice D

option number c is the right answer.