Final answer:
The query relates to Physics and covers the college-level topic of a spring-mass-damper system under harmonic force. It addresses steady state motion that arises after transient effects fade and the system oscillates due to the continuous harmonic input.
Step-by-step explanation:
The subject matter in question involves a spring-mass-damper system with the application of harmonic force and falls under the category of Physics.
This is a college-level question due to the complexity of the concepts, which include Simple Harmonic Motion (SHM), damping, and resonance in an engineering context.
A spring-mass-damper system consists of a mass attached to two identical springs and a damper.
The system is acted upon by a harmonic force, which involves oscillations and damping. In this scenario, the mass is 20 kg, spring stiffness k is 200 N/m, and the damping coefficient c is 125 N·s/m.
The harmonic force applied is f(t)= 90 cos 6t.
To analyze the steady state motion of this system, we examine the behavior as the system oscillates at a frequency where the input and output signals are sinusoids of the same frequency.
The motion reaches a steady state when the effects of the initial conditions have dissipated and the ongoing response to the harmonic force prevails.