Question

A partial of mass m moves in the xy plane so that its position vector is r=acos(wt)i+basin(at)j where a,b and w are constants and a>b. Find the kinetic energy (i)at x=a,(ii)at y=b,(iii) work done I moving the particle from x=a to x=b

Answer 1

1)

$$K=0.5ma^2\omega^2$$

2)

$$K=0.5mb^2\omega^2$$

3)

$$K=0.5m(b^2-a^2)\omega^2$$