How to Solve a Three Mass Four Spring System for Transverse Vibration

[mezacom]

Homework Statement

Three equal masses are attached to a string at equal distances from one another and from the ends, which are rasten to supports so that there is a tension T in the string. Compute normal modes and natural frequencies of small transverse vibrations about equilibrium. Describe the normal modes.
HINT: Assume the tension constant, neglect gravity and asume the string weightless.

similar systems:
https://ccrma.stanford.edu/CCRMA/Courses/152/vibrating_systems.html

Homework Equations

The Attempt at a Solution

 

[tiny-tim]

Welcome to PF!

Hi mezacom! Welcome to PF!

This is a Three-Mass, Four-Spring System, like the Two-Mass, Three-Spring System in your link.

Show us what you've tried, and where you're stuck, and then we'll know how to help!

 

[mezacom]

I know how to solve a three mass four spring system for longitudinal vibration. I have solved it and photo it and you can find it in the link.
I also photo how I think I should start my exercise with transversal vibration.
Did I start solving my problem correctly.
I don’t know how to get rid of all thetas.

http://www.mypicx.com/05272010/mass_spring_solved/