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:
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:
Show 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.
- transient response
steady-state response
- harmonic response
non-transient response
The Correct Option is A
Solution and Explanation
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.
\[\boxed{\text{Transient response}}\]
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\includegraphics[width=0.5\linewidth]{57.png}
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\includegraphics[width=0.5\linewidth]{57.png}
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\includegraphics[width=0.5\linewidth]{57.png}
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