Simple Harmonic Motion

Physics Explaining Oscillating Springs and Pendulums

Jun 26, 2007

Simple harmonic motion is the oscillatory motion of springs, pendulums, and other devices that have a restoring force proportional to the displacement.

Springs

Hang a mass on the end of a spring. It will come to rest at the position which is called the equilibrium position. Pull down on it a little so that it is displaced from its equilibrium position and watch what happens. The resulting oscillatory motion is an example of simple harmonic motion.

Some simple experimentation with a stop watch will show that the time required for one complete oscillation, called the period, does not change when the amplitude (the maximum distance from the central equilibrium point) of the oscillation changes. However the period of the oscillation will change if the amount of mass oscillating changes or if a different spring is used.

Condition for Simple Harmonic Motion

Not all oscillatory motion is simple harmonic motion. When a spring is pulled away from its equilibrium position, the spring pulls back with a restoring force. In a spring this restoring force is directly proportional to the distance that the spring is displaced from the equilibrium position. The restoring force equals a constant value multiplied by the distance the spring is displaced from the equilibrium position.

The constant value is a property of the spring and is called the spring constant. A stiffer spring will have a larger number for the spring constant. This force law for springs is Hooke's law.

Any physical situation in which an object has a restoring force that is proportional to the displacement, as in Hooke's law, will produce simple harmonic motion. A physical situation that has a restoring force that does not follow Hooke's law will produce oscillatory motion that is not simple harmonic motion.

Pendulums

A pendulum swinging through an angle that is not too large is another good example of simple harmonic motion. For small angles, the gravitational force pulling the pendulum back to its central equilibrium position (hanging straight down) is proportional to the distance from the equilibrium position, so it meets the condition for simple harmonic motion. If the pendulum swings through a large angle however, the restoring force is not proportional and the pendulum is not swinging in simple harmonic motion.

As Galileo discovered in church, the period of a pendulum (time required for a complete oscillation) does not depend on the amplitude of the angle it swings through. It also does not depend on the amount of mass hanging on the pendulum. It does however depend on the length of the pendulum.

Simple Harmonic Motion and Clocks

In general the period for one complete oscillation of any object in simple harmonic motion does not depend on the amplitude of the motion. That is why pendulums and springs are used in watches and clocks. Simple harmonic motion is an accurate timing device.