How Do You Model and Solve a System of Three Masses Connected by Springs?

[ggilvar99]

1. There is a central mass Mc connected by two identical springs of spring constant k to two identical masses Mo.

a) Set up and solve the equations for the two normal modes (the ones in the attached images) in which the masses oscillate along the line joining the centers.

Homework Equations

The Attempt at a Solution

I don't know where to begin. The only examples of coupled mass-spring oscillations I have seen are the ones with 2 masses and 3 springs mounted to immovable walls.

 

[Simon Bridge]

I don't know where to begin. The only examples of coupled mass-spring oscillations I have seen are the ones with 2 masses and 3 springs mounted to immovable walls.

This one is done much the same way.
Start with free body diagrams for each mass, work out the forces by Hook's law, get the resulting equation of motion.