How Do You Model a Block Attached to Springs in a Frictionless Box?

[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)

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?

 

[ehild]

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)
View attachment 196327

Homework Equations

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

The Attempt at a Solution

[/B]
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?

You need the change of lengths of the springs when the block is removed from the central position. Each string is fixed to the middle point of the wall, so you need the distances of the block from these middle points. The forces act along the springs, break each force up the vertical and horizontal components.