Question

Figure $1$

As shown in the Figure $1,$ the system consists of rigid body AOJ pivoted at $O$ supported by two springs $(k_1,k_2)$ and two dampers $(c_1,c_2)$ located on two uniform discs. The system is also loaded with two concentrated masses $(m_1,m_2).$ By using MATLAB script, determine and solve the following problems.

a$.$ The natural frequency of the system, ${}_n.$

b$.$ The damping ratio, $.$

c$.$ The period of the vibration, $T_d.$

d$.$ The amplitude ratio, $\frac{x_n}{x_0},$ when $n=1,2,3,4.$