Simple Harmonic Motion

The motion of an oscillating particle depends on the restoring force producing it. One such force is the spring force described by Hooke's Law,

= - k

This means that the force, , always acts in exactly the opposite direction of the displacement from the equilibrium, . Here k is the spring constant with units of N/m.

Let's suppose we have a mass on a horizontal frictionless surface connected to spring. If we pull the mass to one side and release it, it will undergo periodic motion. This motion is called simple harmonic motion (SHM).

SHM describes displacement from the equilibrium position. The maximum displacement is called the amplitude (A) of the oscillation. The displacement will vary from -A to +A.

The motion is also described by its period (T) and frequency (f). T is the time to complete one round trip, and f is the number of round trips per second. Note that f = 1/T. The unit of frequency is the Hertz (Hz) which is one cycle per second (s^-1). The definition of these terms is exactly the same that was introduced in circular motion.

In the movie above, the red mass is undergoing SHM.