Y=y(x) of a particle on the xy plane experience F=-kr

[Animastryfe]

Homework Statement

Assume a particle of mass m which is free to move on the plane x-y. The particle is
experiencing a force F = −kr towards the origin. Find the equation y = y(x) that
describes the motion of this particle on the plane.

Homework Equations

F = ma = -kr

r(t) = A_{1}cos(wt) i + A_{2}cos(wt) j
The 'i' and 'j' above should be unit vectors in the x and y direction, respectively.

The Attempt at a Solution

I think I'm supposed to use the r(t) formula above to isolate x, then substitute it back into the equation to get y?

 

[RoyalCat]

You have two second-order differential equations, one for the motion in the x plane, and another for the motion in the y plane. you are missing two initial value constants.

 

[Animastryfe]

Thank you for the reply. I figured it out shortly after.