# Find the period of the motion and the farthest distance from equilibrium

discordplus

## Homework Statement

an object of mass m experiences a force of the form
Fx = -kx
Fy = -ky

Its initial speed is v and at that time it is at (x,y) = (0,0)

Find the period of the motion and the farthest distance from equilibrium

## Homework Equations

U = -$$\int F(r) dr$$
T = 2$$\pi$$$$\sqrt{m/k}$$

## The Attempt at a Solution

I think this is a superposition of SHM, so the period would just be 2pi root(m/k), yes?

Furthermore since the force acting on the particle is conservative it has a potential energy given by .5kr^2 and its initial energy is .5mv^2, so when its speed equals zero the potential energy is maxed so .5kr^2 = .5mv^2? v is again the initial speed

What happens if the k's in the force equation aren't equal though? In terms of the period i mean. Is the motion just characterized by two separate periods? One in x and one in y?

'Sounds reasonable to me. That also sounds reasonable. 