Does a steady-state response of the differential equation exist for the following?

(a) \(3 \ddot{x}+2700 x=20 \sin 30 t\)

(b) \(3 \ddot{x}+40 \dot{x}+2700 x=20 \sin 30 t\)

(c) \(3 \ddot{x}+2700 x=20 \sin 10 t\)