Springs and masses connected together in a line

[iiJDSii]

Homework Statement

So there are 4 masses in a line. They are connected by 3 springs between them, denoted by k_12 & l_12 (spring coefficient + natural extension length), k_23 & l_23, etc.

Homework Equations

Write down the f = ma equations of motion for all 4 masses.

The Attempt at a Solution

See my image.



This problem really annoys me because I always learn how to do it for the test but never remember. I think I've gone through 3 courses where this problem came up and every time I could never remember. Well now it's just a random exercise in a linear algebra text I'm reading and I wouldn't mind learning it right once and for all. After all I'm supposed to be an engineer.

Thank you for any help.

 

[Simon Bridge]

Well do you really need to memorize the problem? Besides, the time you do, someone will give you one with 5 or 3 masses, or springs with varying k :)

It's like this one only with four masses instead of two. (You could use the Hamiltonian or Lagrangian mechanics of course.)