SHM
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Simple harmonic motion (S.H.M.)
Simple harmonic motion is the simplest form of vibratory or oscillatory motion.
(i) S.H.M. are of two types
(a) Linear S.H.M.
When a particle moves to and fro about a fixed point
(called equilibrium position) along a straight line then m
its motion is called linear simple harmonic motion.
Example : Motion of a mass connected to spring.
(b) Angular S.H.M.
When a system oscillates angularly with respect to a fixed axis then
its motion is called angular simple harmonic motion.
Example :- Motion of a bob of simple pendulum
(ii) Necessary Condition to execute S.H.M.
(a) Motion of particle should be oscillatory.
(b) Total mechanical energy of particle should be conserved (Kinetic energy + Potential energy = constant)
(c) Extreme position should be well defined.
(d) In linear S.H.M.
The restoring force (or acceleration) acting on the particle should always be proportional to the
displacement of the particle and directed towards the equilibrium position
Negative sign shows that direction of force and acceleration is towards equilibrium position and y is
displacement of particle from equilibrium position.
(e) In angular S.H.M.
The restoring torque (or angular acceleration) acting on the particle should always be proportional to the
angular displacement of the particle and directed towards the equilibrium position
Comparison between linear and angular S.H.M.
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