Question $3$:

Consider the following system:

Note:

$J_1=J_0,J_2=2J_0$

$k_{t1}=k_{t2}=k_t$

$k_{t3}=0$

Write the equations of motion of the system $($free vibration$)$

Assuming harmonic motion with the same frequency, the same phase and different amplitudes, find:

$2\mathrm{.}1)$ the two natural frequencies of the system

$2\mathrm{.}2)$ the two corresponding modes in terms of the ratios $r_1$ and $r_2$

$2\mathrm{.}3)$ Explain what the ratios $r_1$ and $r_2$ mean in terms of the vibration of the two discs.