How Does Spring Configuration Limit Mass Movement in Physics?

[cscott]

Homework Statement

Say you have a mass in the center of a room (equilibrium (x,y) = (0, 0)) that is connected to one wall via a spring along -x axis and to another wall via a spring along -y axis (the axes are parallel with each wall, respectively.) If I know F(x,y) and the velocity at a point, after the mass is set in motion with an initial velocity at some other point is there any way to figure out which region of the floor the mass will be restricted to?

The Attempt at a Solution

No ideas here...

 

[Avodyne]

What is F(x,y) supposed to be?

 

[cscott]

What is F(x,y) supposed to be?

F(x,y) = force vector

sorry.

 

[Avodyne]

Is F the force produced by the springs, or some other force?

 

[cscott]

By the springs

 

[Gokul43201]

Homework Statement

Say you have a mass in the center of a room (equilibrium (x,y) = (0, 0)) that is connected to one wall via a spring along -x axis and to another wall via a spring along -y axis (the axes are parallel with each wall, respectively.) If I know F(x,y) and the velocity at a point, after the mass is set in motion with an initial velocity at some other point is there any way to figure out which region of the floor the mass will be restricted to?

Yes, you can know the path of the mass if you know two velocities, and you also know both components of F(x,y).

Can you write down the differential equations governing the motion of the mass in (x,y)?