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Dafe

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## Homework Statement

Suppose masses [tex]m_{1}, m_{2}, m_{3}, m_{4}[/tex] are located at positions [tex]x_{1}, x_{2}, x_{3}, x_{4}[/tex] in a line and connected by springs with constants [tex]k_{12}, k_{23}, k_{34}[/tex] whose natural lengths of extension are [tex]l_{12}, l_{23}, l_{34}[/tex].

Let [tex]f_{1}, f_{2}, f_{3}, f_{4}[/tex] denote the rightward forces on the masses, e.g.,

[tex]f_{1} = k_{12}(x_{2} - x_{1} - l_{12})[/tex]

a) Write the 4 X 4 matrix equation relating the column vectors [tex] f [/tex] and [tex] x [/tex]. Let [tex] K [/tex] denote the matrix in this equation.

## Homework Equations

## The Attempt at a Solution

I'm trying to find the rightward force acting on every mass as the springs are stretched.

[tex]f_{2} = k_{23}(x_{3} - x_{2} - l_{23}) - f_{1}[/tex]

[tex]f_{3} = k_{34}(x_{4} - x_{3} - l_{34}) - (f_{1} + f_{2})[/tex]

[tex]f_{4} = f_{1} + f_{2} + f_{3}[/tex]

It seems quite complicated to put this into matrix form, so I'm assuimg that I've done something wrong.

Suggestions?