Question

obtain the differential eyutio of linear s.h.m
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Answer 1

Answer:

A mass on a spring can be considered as the simplest kind of Simple Harmonic Oscillator.

With a displacement of x on mass m , the restoring force on the spring is given by Hooke's law, withing the elastic limit, F=-kx where k is the spring constant.

Newton’s Second law in the x-direction in differential form therefore becomes,

m

dt

2

d

2

x

=−kx

or

dt

2

d

2

x

=−

m

k

x

The above equation represents the differential form of SHM .

Here the spring force depends on the distance x, the acceleration is proportional to the negative of displacement.