The displacement vector of a particle of mass m is given bya) show that the trajectory is an ellipse b) show that

contexto.120

3 years ago

a)
$\begin{array}{l} r(t)=\hat{i} A \operatorname{coswt}+\hat{j} B \sin \omega t \\ x=A \cos \omega t \\ y=B \sin \omega t \\ x / A=\cos \omega t \\ y / B=\sin \omega t \end{array}$
Squaring both the equations and adding them,

The above equation is of an ellipse and so the trajectory is an ellipse.
b)

Solving the above, we get