Problem 67 - Precalculus Essentials

Question

What is simple harmonic motion? Give an example with your description.

Step-by-Step Solution

Answer

Simple harmonic motion (SHM) is a repetitive motion where the force is directly proportional to the displacement and acts in the opposite direction. It features include the object trying to return to a fixed point and the magnitude of velocity and acceleration varies with the position. An example is the motion of a simple pendulum.

Step 1: Understanding simple harmonic motion

Simple harmonic motion (SHM) can be defined as a motion that repeats itself after an equal interval of time. It is the form of oscillatory or periodic motion where the restoring force is directly proportional to the displacement and acts in the direction opposite to the displacement.

Step 2: Characteristic features

There are some characteristic features of SHM. It is always produced by a restoring force which means the object always tries to return to a fixed point or equilibrium point. The magnitude of the velocity of the particle performing SHM is highest at the mean position, zero at the extreme position. The acceleration of the particle is highest at the extreme position, and zero at the mean position.

Step 3: Example of SHM

An often cited example of simple harmonic motion is the motion of a simple pendulum. As the pendulum swings back and forth, the motion repeats at regular intervals. The pendulum tries to return to its equilibrium point due to the force of gravity acting upon it. However, at the extreme position it has the maximum potential energy and at its mean position it has the maximum kinetic energy.