1. A 2-DOF system is shown in Figure 1. The mass of m₂ is acted by the external force f(t) =

fo sin(wt) and the system is also excited by xp (t) = xo sin(wt) through the left massless plate.

The system parameters are given as m₁ = 4m₂ = 16 kg, c = 200 N-s/m, k₁ = 2k2 =

100 kN/m, fo = 10 kN, xo = 1 m, and w = 200 rad/s. The initial conditions are given as

x₁ (0) = 0.5 m, x₂ (0) = 0 m, x₁ (0) = 0 m/s, and x₂ (0) = 20 m/s. For the given information,

solve the following problems:

(a) The coordinates of x₁ and x₂ are the displacements of m₁ and m2, respectively. Draw the free-

body diagrams (FBDs) of m₁ and m₂, and derive EOMs by applying the Newton's 2nd Law of

Motion to the FBDs. Write the EOMs in a matrix form in terms of mass matrix, M, damping

matrix, C, and stiffness matrix, K.