Introduction to Simple Harmonic Motion

The needle of a pendulam clock moves circularly on the same path.

But the bob of the pendulum itself moves to and fro on the same path.

If a body performs repetitive to and fro motion about a zero position or equilibrium position, we say it oscillation.

The repetitive to and fro motion of the pendulum is an oscillatory motion, we say it Simple Harmonic Motion.

Let’s know more about motion of the pendulum bob.

Now we have located the positions of the pendulum bob with letters a,b,c,d,e,f and g respectively.

Let’s assume displacement to the right of the zero position is positive.

And the displacement to the left of the zero position is negative.

The position of the pendulum bob measured along the arc relative to the rest position is a function of the sine of the time.

The maximum displacement of the bob from the center of the oscillation is amplitude of the oscillation.

And the number of oscillation covered by the bob per unit of time is angular frequency, let’s represent it by a symbol $\omega$.

This is the relation between angular frequency and time period $T$ which is the time to cover one complete oscillation.

Let’s know more about Simple Harmonic Motion.

Simple Harmonic Motion is a type of oscillatory motion.

This is the displacement equation of a Simple Harmonic Motion in which we represent $x$ as displacement.

In displacement equation $t$ represents the time and $\varphi$ represents the phase constant respectively.

The quantity ($\omega t+\varphi$) is time-varying quantity. We say its phase of the motion.

The phase constant depends on the displacement and velocity at the instant $t=o$. It is the time when we start the measurement.

We also say phase constant as initial phase.

Revision

Simple Harmonic Motion is a type of oscillatory motion.

The displacement equation of a Simple Harmonic Motion is represented by:

The maximum displacement of the bob from the center of the oscillation is amplitude of the oscillation.

The End