Show that the equation `x=Asinomegat` represents a simple harmonic motion.

Explanation

Equation of displacement is, `x=Asinomegat`
`therefore` Velocity, v = `(dx)/(dt)=omegaAcosomegat`
and acceleration, `a=(dv)/(dt)=-omega^(2)Asinomegat=-omega^(2)x`.
Now, from the equation, `a=-omega^(2)x`, it is evident that (1) the acceleration of the particle is proportional to the displacement and (2) the direction of acceleration is opposite to that of displacement, i.e., the acceleration is directed towards the position of equilibrium. So, by definition, it is a simple harmonic motion.