Answer to Question #207355 in Classical Mechanics for Aysu

Question

 A particle of mass m moves according to laws x=A·cosωt and y=B·sinωt. Find the force acting on thisparticle in each point of its trajectory.

Answer 1

$$\bold{r}=a \cos ωt\bold{i }+ b \sin ωt\bold{j}\\ \bold{v}=b\omega \cos ωt\bold{j }-a\omega \sin ωt\bold{i}\\ \bold{a}=-\omega^2(a \cos ωt\bold{i }+ b \sin ωt\bold{j})=-\omega^2\bold{r}\\ \bold{F}=-m\omega^2(a \cos ωt\bold{i }+ b \sin ωt\bold{j})=-m\omega^2\bold{r}\\$$