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.