Find the magnitude and direction of the force acting on the particle of mass m during its motion in the plane `xy` according to the law `x=a sin omega t`, `y=b cos omega t`, where a, b, and `omega` are constants.

Explanation

Obviously the radius vector describing the position of the particle relative to the origin of coordinate is
`vecr=xveci+yvecj=a sin omega tveci+b cos omega t vecj`
Differentiating twice with respect the time:
`vecw=(d^2vecr)/(dt^2)=-omega^2(a sin omega t veci+b cos omega t vecj)=-omega^2vecr` (1)
Thus `vecF=mvecw=-momega^2vecr`