Question

Show that simple harmonic function may be regarded as the projection of uniform circular motion along a diameter of the circle. Hence derive an expression for the displacement of a particle in S.H.M.

Answer 1

Using Newtons second law of motion and the expression for acceleration of a particle undergoing S.H.M., the force acting on a particle of mass M in S.H.M. is:

f(t) = ma

= -mω² (xt)

i.e., f(t) = -kx (t)

where k = mω²

or \(\omega = \sqrt{\frac{k}{m}}\) 

Like acceleration, force is always directed towards mean position.