Simple Harmonic Motion and its Application to a System

Question

What is simple harmonic motion? How can it be applied to a real system?

Answer

SHM is motion that occurs when the driving force acting on an object is directly proportional and acting in an opposite direction to the displacement of the object. This is observed when a mass is hanging from a spring, or can be used to approximate the motion of a pendulum. The motion is periodic, following a sine curve, with an amplitude that represents the maximum displacement and a frequency which is dependent on the parameters of the system.
Simple Harmonic Motion is representative of a theoretical model in which there is no internal friction. In order to consider a real situation, damping must be applied so that amplitude decreases over time. Damping is represented by a frictional force acting against and directly proportional to the velocity of the object. There are three types of damped system:

• Over Damped: The object returns to equilibrium without oscillating, over time.
• Critically Damped: The object returns to equilibrium without oscillating in the shortest time possible.
• Under Damped: The object oscillates, and the amplitude slowly decreases to zero.

By applying additional force to an object under simple harmonic motion, the model becomes more complex. If the force applied is periodic and matches the resonant frequency of the original system, then large amplitudes will be achieved.

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