Question

Generally speaking, a system undergoes simple harmonic motion if there is a restoring force that increases linearly with displacement from equilibrium. In the discussion, describe how a pendulum and a mass on a horizontal spring satisfy those conditions (ignore any friction forces); also, include another example of a real world system that undergoes simple harmonic motion and discuss how it satisfies the conditions mentioned above. Finally, be sure to respond to at least two of your peers’ discussion posts.

Answer 1

For a spring system, the force applied by the spring is given by,

Hence we can say that for a spring system the force applied by the spring in the opposite direction of displacement is equal to the amount of displacement. For a pendulum we can write at a extreme height position, we can write the force on the pendulum as,

In the case of pendulum also the force is directed towards the direction where the angle of the pendulum decreases (hence negative value), Hence in this case also the restoring force is directly proportional to the displacement.

In all the cases where the restoring forces are directly proportional to the displacement the system undergoes simple harmonic motion.

Real life example is an example of tuning fork, in that case the restoring force will be the stress created in the material which makes it to come back to normal position. This causes the restoring force to be dependent on the displacement, and hence the tuning fork will undergo simple harmonic motion.