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Simple Harmonic Motion

 

 

Simple Harmonic Motion (SHO)

 

Ø Any vibrating system for which the restoring force is directly proportional to the negative of the

         displacement is said to exhibit simple harmonic motion.

 

Ø Simple harmonic motion is typified by the motion of a mass on a spring subject to the linear

         elastic restoring force given by Hooke's Law.  F = -kx

 

         F = restoring force

         k = spring constant

         x = displacement

 

Ø Note that F is not constant - it varies with position

 

Ø The equations will be discussed in subsequent sections

 

 

 

Some Terminology

Ø The motion is sinusoidal in time - characterized by a sine wave

Ø The position with no force applied is called the equilibrium point - horizontal line on
        the right

Ø The distance of the mass from the equilibrium point is called the displacement

Ø The greatest displacement from the equilibrium point is called the amplitude, A

Ø A cycle is the complete motion from some initial point back to that point - a high
       to a subsequent high, for example

Ø The period, T, is the time required to complete one cycle

Ø The frequency, f, is the number of complete cycles per second. f = 1/T.

Ø Frequence is is measured in hertz (Hz), which is defined as 1 cycle per second

 

 

Some of the Many Examples of Simple Harmonic Motion