Consider the viscoelastically damped system of Figure. The system differs from the viscously damped system by the addition of the spring k1, which introduces one more coordinate, x1' to the system.
The equations of motion for the system in inertial coordinates x and x1 are
mx"= -kx-c(x'-x'1)+F
0= c(x'-x'1) - k1x1
Write the equation of motion in matrix form.
