[QUE/CM-01012#Solu] -- Motion on Curves (Solved)

A particle of mass $m$ moves on a cycloid under influence of uniform gravitational field. The parametric equations of the cycloid are given by $$ x= R( \phi + \sin\phi) , \qquad y=R(1-\cos\phi).$$ Find a suitable transformation to show that the equations of motion is identical to that of a simple harmonic motion  with frequency $\omega=g/4R$.

Source{Sommerfeld}