The mass m is coupled to the support A, which is displacing harmonically according to y =...

The mass m is coupled to the support A, which is displacing harmonically according to y = Y sin ω0t, by the linear elastic spring of constant k and the dashpot with constant c.

(a) Derive its equation of motion, using x as the independent variable, and explain in what way the resulting equation of motion is not in the form of Eq. (9.71).

(b) Next, let z = x − y and substitute it into the equation of motion found in part (a). After doing so, show that you obtain an equation of motion in z that is of the same form as Eq. (9.71).

(c) Find the steady-state solution to the equation of motion found in part (b) and then using that, determine the steady-state solution for x.

Figure P9.55