Question

A point moves in X−Y plane according to X=a sin(wt) and Y=a (1−cos(wt)). What path will the particle follow?

Answer 1

This is a circle of radius `abs a`, centred on `X,Y = 0, a`

Explanation:

`X=a sin(wt), qquad Y=a (1−cos(wt)`

`implies sin omega t = X/a, qquad cos omega t = 1- Y/a`

From the Pythagorean identity:

`(X/a)^2 + ( 1- Y/a)^2 = 1`

`(X/a)^2 + ( Y/a - a/a)^2 = 1`

`X^2 + ( Y - a)^2 = a^2`

This is a circle of radius `abs a`, centred on `X,Y = 0, a`