Explanation of Periodic Motion

Periodic motion

Any motion which repeats itself after a definite interval of time is called periodic motion. A body performing periodic motion goes on repeating the same set of movements. The time taken for one such set of movements is called its period or periodic time. At the end of each set of movements the state of the body is the same as that at the beginning.

Examples: the motion of the moon around the earth, the motion of the planets around the sun, the motion of electrons around the nucleus. Uniform circular motion is therefore also a periodic motion.

Oscillatory (vibratory) motion

Another type of periodic motion, in which a particle repeatedly moves to and fro along the same path, is called oscillatory or vibratory motion.

• Every oscillatory motion is periodic, but every periodic motion need not be oscillatory.
• Circular motion is periodic but it is not oscillatory, because the particle does not move to and fro along the same path.

Simple harmonic motion

The simplest form of oscillatory periodic motion is simple harmonic motion, in which every particle of the oscillating body moves to and fro about its mean position along a certain fixed path.

• If the path is a straight line, the motion is called linear simple harmonic motion.
• If the path is an arc of a circle, it is called angular simple harmonic motion.

Period and frequency

• Period $T$: the smallest interval of time after which the to and fro motion is repeated. SI unit: second (s).
• Frequency $n$: the number of oscillations completed per unit time. SI unit: hertz (Hz).

Standard results

• $n=\dfrac{1}{T}$
• $\omega=2\pi n=\dfrac{2\pi}{T}$, where $\omega$ is the angular frequency in rad/s