**Oscillations – Notes**

**Periodic and oscillatory motions**

Motion which repeats itself after a fixed interval of time is called periodic motion.

The to-and-fro motion of a body is called oscillatory motion.

All oscillatory motions are periodic motions. But every periodic motion need not be an oscillatory motion.

Simple harmonic motion is the to-and-fro motion of body where the force is always directed towards the mean position and is proportional to the displacement but in the opposite direction.

**Period, frequency and displacement**

Time period, T = Time taken/Number of Oscillations

Frequency, n = Number of Oscillations/ Time taken

n=Number of oscillations/Time taken

n=1/T

The displacement variable in general can be understood as the variations in physical quantity with time in a border sense when the variable involved oscillates.

A linear combination of two periodic functions is also periodic.

Any periodic function can be expressed as a superposition of sine and cosine functions with suitable coefficients.