Finding the Equations of Motion for a Mass-Spring System

[lz975545]

Homework Statement

A block is attached to the sides of a square box by 4 springs. The box is placed horizontally on a frictionless surface (ignore gravity). The mass of the block is $m$, the natural length of each spring is $l$, and the strength of each spring is $k$. Place the block at $(0,0)$. Let $x(t), y(t)$ the position of the block in time. Find the equations of motion of the block. (Use vectors to break each force up into its vertical and horizontal components)
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Homework Equations

$F = m\frac{d^2x}{dt^2} = -kx$

The Attempt at a Solution

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I'm just a little confused on how to start this problem. Would I use the distance formula from each wall to the block (wall to block to wall) on each axis?

 

[Chestermiller]

I'm just a little confused on how to start this problem. Would I use the distance formula from each wall to the block (wall to block to wall) on each axis?

Yes. If the coordinates of the block are (x,y), what are the lengths of the 4 springs? What is the change in length of each spring? What are magnitudes of the 4 forces? In terms of the unit vectors in the x and y directions (and x and y), what are the 4 unit vectors in the directions of the springs?