Define linear S.H.M. Obtain differential equation of linear S.H.M.

Updated on : 2022-09-05
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Linear SHM is the simplest Kind of oscillatory motion in which a body when displaced from its mean position, oscillates 'to and fro' about mean position and the restoring force (or acceleration) is always directed towards its mean position and its magnitude is directly proportional to the displacement from the mean position.
Consider particle moving along the circumference of a circle of radius 'a' with a uniform angular speed of in the anticlockwise direction.
Refer image .1

Particle along the circumference of the circle has its projection particle on diameter at point . This projection particle follows linear SHM along line when particle P rotates around the circle.

Let the rotation start with initial angle as shown above
In time 't' the angle between OP and X-axis will become as shown below:
Refer image 2

Now from  

Differentiating above equation with respect to time 
we get velocity

Differentiating again we get acceleration


Equation (1),(2) and (3) are differential equations for linear SHM.

Solve any question of Oscillations with:-
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