X3 k3 k 000 000 000 m m2 m3 For the following, derive the EOMs by hand. Then use MATLAB to solve and plot the results. Solve using the analytical methods specified to obtain the "exact" solutions (do not use ode45, unless you want to compare analytical vs numerical solutions). Problem 6.99 Find the steady-state response of the system shown with k = k = k3 = k4 = 100 N/m, c = C = C3 = C4 = 1 N-s/m, m = m = m3 = 1 kg, F(t) = Fo cos wt, Fo = 10 N, and w = 1 rad/s. Assume that the spring k4 and the damper c4 are connected to a rigid wall at the right end. Use the mechanical impedance method described in Section 5.6 for solution. Plot the response of the DOFS versus time. Problem 6.99 Modal Repeat problem 6.99 but use proportional damping with a = 0 and = 0.01. Find the steady-state response using the modal superposition method. Plot the response of the DOFS versus time.