Question

When there is a reduction in amplitude over every cycle of vibration, then the body is said to have

• A. free vibration
• B. forced vibration
• C. damped vibration
• D. underdamped vibration

Hint:

Any system losing energy per cycle exhibits damped vibration.

Answer 1

The Correct Option is C

In an ideal undamped vibration, no energy leaves the system, so the amplitude stays exactly the same forever, cycle after cycle.
The question instead describes amplitude that keeps shrinking, meaning energy is being lost from the system on every cycle, which can only happen if some resisting (damping) force, like friction or a dashpot, is acting.
This continuous loss of energy per cycle, and the resulting steady decay in amplitude, is exactly what defines damped vibration, regardless of whether the specific case is underdamped, critically damped, or overdamped.
Since only the general presence of energy dissipation is described, without stating whether oscillation continues or how strong the damping is, the matching term is damped vibration.

Answer 2

Picture the displacement-versus-time waveform for each type of vibration. Undamped free vibration traces a plain, unchanging sine wave. Forced vibration in steady state traces a wave of constant amplitude set by the driving force. Only one type of waveform shows a shrinking envelope from cycle to cycle. Testing each option against this picture:

1. Free vibration: Without any specified damping, its waveform is a level, constant-amplitude sine curve, not one with a shrinking envelope, so this alone does not depict the described decay.
2. Forced vibration: Its steady-state waveform also settles into a constant-amplitude curve dictated by the driving frequency and force, not a curve whose peaks get progressively smaller.
3. Damped vibration: Its waveform is a sine curve enclosed within a decaying exponential envelope, with each successive peak smaller than the last, exactly matching a plot of amplitude shrinking cycle by cycle.
4. Underdamped vibration: Its waveform looks similar to damped vibration's decaying envelope, but the term additionally commits to there being visible oscillation (as opposed to overdamped, non-oscillatory decay); the question does not specify this extra detail, so the general term describing the decaying-envelope waveform is the better fit.

The shrinking-envelope waveform matches the general description of damped vibration.

Therefore, the correct answer is damped vibration.