Question

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:

• A. transient response
• B. steady-state response
• C. harmonic response
• D. non-transient response

Hint:

In vibration problems, always separate total response into transient (dies out) and steady-state (persists). Only the transient part is affected by damping decay.

Answer 1

The Correct Option is A

Step 1: General solution of forced vibration.
The displacement of a damped, harmonically forced system is \[ x(t) = x_{\text{transient}}(t) + x_{\text{steady}}(t). \] 

Step 2: Nature of each part.
- The transient response is due to initial conditions and decays exponentially because of damping. - The steady-state response is the long-term periodic motion at the forcing frequency, which persists. 

Step 3: Identification.
Since damping causes exponential decay, the response that disappears with time is the transient response.

 \[\boxed{\text{Transient response}}\]