Question

A particle simultaneously participates in two mutually perpendicular oscillators $x=\sin \pi t$ and $y=2\cos 2\pi t$. Write the equation of trajectory of the particle.

Answer 1

$x=\sin \pi ty=2\cos 2\pi t$

As

$\cos 2\theta =-2{\sin }^2\theta +t$

So

$y=2(-2{\sin }^2\pi t+1)$

Putting the value of $x$ in the above equation we get,

$y=-2(2x^2-1)y=-4x^2+2$