Simple Harmonic Motion (S.H.M)
Class : 12
We all are familiar with periodic motion, i.e. the motion which repeats itself at equal intervals of time. A few common examples of periodic motion are the motion of simple pendulums and compound pendulums, the motion of electrons in their orbits, motion of planets around the sun, vibration of stretched wires, motion of a mass attached to a string etc. The interval of time after which the motion is repeated is called time period of the motion. If a particle in periodic motion has to and fro motion over the same path, is called Oscillatory or vibratory motion. The motion of a mass spring system, motion of simple pendulum, vibration of atoms at their lattice sites are a few examples of oscillatory motion. Most of the oscillatory motions in nature are simple harmonic motions (s.h.m.).
The vibration of atoms at the lattice sites are approximate simple harmonic. The oscillation of simple pendulum is simple harmonic when its amplitude is small. The motion of air molecules when sound waves pass through it is simple harmonic.
Definition of s.h.m :
It is defined as the motion in which the acceleration is always directed towards the mean position (a fixed point) and is directly proportional to the displacement from the mean position.
The displacement y of a particle executing s.h.m. at any instant t is given by,
Where, ‘a’ is amplitude of the motion. W is uniform angular velocity. w =2πf, where, f is frequency of vibration. Also, T = 1/f = 2π/f, is period of the motion. The displacement-time curve for s.h.m. is cine curve as shown in figure. Like mechanical oscillating system, visible light waves, radio waves, microwaves are oscillating electric and magnetic field vectors. These are electromagnetic oscillating systems. The electromagnetic oscillations are described by the same mathematical equations. In an electromagnetic wave, y in equation (1) may represent the component of the electric or magnetic field vectors at a certain instant.
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