Since most of the vibrating system follow harmonic motion (SHM), therefore it is essential to have proper understanding of SHM related basic concepts.

A body is said to have simple harmonic motion (SHM), if it moves or vibrates about a mean position such that its acceleration is always proportional to its distance from the mean position and is directed towards the mean position or equilibrium position.

#### Differential Equation of SHM

Consider a particle **‘P’** moving around a circle with a uniform angular velocity **ω** rad/s as show in fig.

Displacement of particle **‘P’** from mean position after time **‘t’**, as shown in fig. is given by

Acceleration of particle after time **‘t’** is

The above equation is known as differential equation or fundamental equation of S.H.M.

Time period and frequency:

Time Period, t_{p}=\frac{2 \pi}{\omega}

Frequency, f=\frac{1}{t_{p}}=\frac{\omega}{2 \pi}

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