Simple Harmonic Motion

Let us consider two simple models - :

1. An apple tied to a string
This is a classic form of a pendulum (in this case – an apple) which will show us the most basic form of vibration.

If the apple is displaced from its mean position, it oscillates around the mean position.

In such a periodic motion, the restoring force is proportional to the displacement and if there were no friction or opposing force, this oscillation will go on forever. This is called free vibration.

The movement of the pendulum(apple) from its mean position can be plotted in a graph against time and follows a well-defined mathematical relationship - A sine Wave

2. A spring and a mass

The spring has a stiffness that makes the unit force deflected over a certain distance - the stiffer the spring the lesser the deflection for the unit force.

The mass (in this case – the apple) has a constant gravitational force pulling it downwards while the spring pulls it back. This system is similar to the pendulum - if the mass is displaced from its mean position it oscillates around the mean position.

This type of oscillatory Movement in both these examples is called the Simple Harmonic Motion which is at the very core of understanding the concept of vibration.

Simply defined the motion is related to circular movement - described by the following equation :

This expression gives you the value of distance (D) as a function of time (t).


What is Natural Frequency?

This is the frequency at which the pendulum will oscillate by itself. It is inversely proportional to the length of the pendulum.

Here is something for you to think about - does the mass of the pendulum or the mass in a spring-mass system affect the natural frequency and why?

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