Simple Harmonic motion

When you hear the term Simple Harmonic Motion a few questions pop in your mind.

What is meant by harmonic motion?

simple harmonic motion
By Mazemaster – Own work, Public Domain, https://commons.wikimedia.org/w/index.php?curid=5803197

Why is it called simple?

When a body oscillates about a mean position under the application of a restoring force then it is termed as a harmonic motion and simple harmonic motion is a part of harmonic motion. Thus, all simple harmonic motions are harmonic motions, but the inverse is not true.

One simple to understand SHM is that the ratio of acceleration and displacement should be constant. Take the example of a spring-mass system. The body starts to oscillate when a force is applied. It has the maximum acceleration at its extreme position and maximum velocity at the mean position. There are multiple examples of SHM but one important point needs to be kept in mind. Say I case of a pendulum the displacement caused by the force should be small for it to displace SHM.

To emphasize this point, assume there to be a hole from one end of the earth to another. Now drop a small mass from one side of that hole and in the second case drop the mass close towards the center of the earth.

Which case would exhibit SHM?

The restoring force would be provided by the gravitation pull. Though both the cases would exhibit harmonic motion, only the second case will show simple harmonic motion.

Take a pendulum clock and a spring-mass system. Now I’ve transported you into space. Now when you provide displacement to both the bodies, which one will exhibit SHM and why?

Only the spring-mass system will exhibit SHM, not the pendulum clock because the clock requires gravity as the restoring force which is not available in the outer space and the spring-mass system provided the restoring force due to the spring.

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