Differential Equation of Simple Harmonic Motion:
Let x be the displacement from the equilibrium position of a particle executing SHM. Then the velocity of the particle is v = dx/dt.
The acceleration of the particle,
a = dv/dt = (d/dt).(dx/dt) = d2x/dt2
So, the equation of SHM can be written as –
d2x/dt2 = -ω2x
or, d2x/dt2 + ω2x = 0 …equ(1)
Equation(1) is called the differential equation of SHM.