# Simple harmonic motion problem involving matrices

## Homework Statement

2 equal masses are joined together by a spring of stiffness k. each of the masses is then connected to a wall with an identical spring. derive the equations of motion in matrix form. (a diagam has 2 masses with x1 on top of the first mass and x2 on top of the second.)

## Homework Equations

hooke's law: F = kx

## The Attempt at a Solution

mass 1:

mx1'' = F(x2 - x1) - Fx1
mx2'' = Fx2 - F(x2 - x1)

^ are these correct?

Mass one looks good but mass two is off. What happened to your third spring ?

Also, draw yourself a free body diagram.

Mass one looks good but mass two is off. What happened to your third spring ?
Also, draw yourself a free body diagram.
i did. there are only 2 displacements (x1 and x2), right? the extension of the third spring is not kx2?

There are only two equations, but you need to include the third spring. If the masses are going to move springs 1,2, and 3 have to move with them.

There are only two equations, but you need to include the third spring. If the masses are going to move springs 1,2, and 3 have to move with them.
but each mass is connected to 2 springs. therefore each equation should only have 2 terms. the only mistake i can see with the second equation is that Fx2 (force from the THIRD spring) should be negative. oh, and sorry if i haven't been clear enough -- the diagram goes like this:

[wall] [spring] [mass 1] [spring] [mass 2] [spring] [wall]

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Mass one depends upon springs 1 and 2. Mass two depends on springs 2 and 3. Rewrite your equations and redraw your FOB.