Step by step solution on this vibration problem please show

Solution

a) moment of inertia of disk 1 m1b^2

moment of inertia for second disc m2 R2^2 where R2 is the radius

b) Assume th mass stiffness matrix is [a1 b[

[ b a2 [

the known eigenvalue and mode shape (eigenvector) can be used to get eqns in a1,b, a2

similarly, the same matrix with unknown eigenvalue and known eigenvector can be set up and two eqns obtained.

Then we have 4 eqns in a1, a2, b and unknown eigenvale. this can be solved for the freq, desired.