Simple harmonic motion problem involving matrices

[ABoul]

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?

 

[CFDFEAGURU]

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

 

[CFDFEAGURU]

Also, draw yourself a free body diagram.

 

[ABoul]

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?

 

[CFDFEAGURU]

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.

 

[ABoul]

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]

 

[CFDFEAGURU]

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