Write the force law for SHM and obtain formula of period of SHM particle.

Explanation

The acceleration of SHM particle
`a(t) = -omega^(2)x(t)" ""………"(1)`
Where x(t) is the displacement at time t.
The force exerted on SHM particle according to Newton.s second law
`F= ma(t)`
`therefore F= -m omega^(2) x(t)" ""........."(1)` [From equation (1)]
The force exerted on SHM is always directly proportional to displacement and towards the mean position. This force is restoring force for SHM
`F propto -x(t)`
`therefore F= -kx(t)" ""........."(3)`
where k is the constant of SHM and is the restoring force per unit displacement comparing equation (2) and (3)
`k= m omega^(2)`
`therefore omega = sqrt((k)/(m))`
Putting `omega =(2pi)/(T)`,
`(2pi)/(T)= sqrt((k)/(m))`
`therefore T= 2pi sqrt((m)/(k))`.