Discussion
For a single degree of freedom spring-mass-damper system subjected to harmonic forcing, the part of the motion (response) that decays due to damping is known as:
Answer: A
The decaying part of the response is the transient response.
Under harmonic forcing, the motion is the sum of two parts. The complementary solution is the system's free vibration, which carries a factor \(e^{-\zeta\omega_{n}t}\) and so dies away with time because of damping: this is the transient. The particular solution oscillates at the forcing frequency with constant amplitude for as long as the force acts: this is the steady-state response.
So the steady-state (non-transient) part is precisely the part that does not decay, and 'harmonic response' describes the forced oscillation at the driving frequency, again the part that persists.
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