Consider a rigid bar with mass Mbar, and mass moment of inertia IG is supported by two springs, with ball of mass MB attached to the bar and ground by two identical springs as shown. Motion of the system is described by three DOFs, i.e., Xc, XB, and 0 A e=0.05 m B Xc Mbar C IG G Ꮎ XB k3 800 N/m WW MBall k3=800 N/m k2 1800 N/m k₁ = 1200 N/m a = 0.20 m b = 0.25 m Knowing that the kinetic and potential energies of the system are 1 1 1 T == Mar (X + eė)² + − MB X 3 + − Ic - C 2 Ball B V = ²±²k,(x − a)² + ²±² k₁₂(X +b0)² 1 1 +k3(X)²+k₁(Xc -XB)² For system properties G Mbar =0.15kg; M Ball = 0.02kg; I = 0.025kg.m k₁ =1200N/m; k₁ = 1800N/m;k = 800N/m a=0.20m; b= 0.15m; e = 0.05m 1. Derive equations of motion using Lagrange's equation 2. Formulate the eigenvalue problem 3. Solve for system eigenvalues and eigenvectors 4. Assuming the following initial conditions |✗¸ (0) = 0.004 m, vg(0) = 0.0; |X (0) = 0.0 m, vc (0) = 0.0; 0(0)=5°, (0) = 0.0 Plot the response of the considered DOFS as a function of time