Three flywheels, no damping

A 6^th order system with three modes of vibration

This system has three linked masses.

For mode 1 IC's → x₁(0)=90,  x₂(0)=128,  x₃(0)=90, slowest frequency
For mode 2 IC's → x₁(0)=-128,  x₂(0)=0,  x₃(0)=128, frequency 1.8 times faster than mode 1
For mode 3 IC's → x₁(0)=90,  x₂(0)=-128,  x₃(0)=90, frequency 2.4 times faster than mode 1