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

Step 1: Understanding vibration behavior.
In vibration systems, amplitude may remain constant or decrease depending on energy loss mechanisms such as friction or damping.
Step 2: Effect of damping.
When damping is present, energy is dissipated in every cycle, causing the amplitude to reduce progressively with time.
Step 3: Eliminating incorrect options.
Free vibration occurs without external force but may or may not include damping.
Forced vibration occurs due to continuous external excitation.
Underdamped vibration is a specific case of damped vibration with oscillations present.
Step 4: Conclusion.
A reduction in amplitude over each cycle indicates damped vibration.

Answer 2

The question describes a system whose amplitude shrinks a little more with every cycle it completes. This behaviour is a direct signature of energy being continuously removed from the system as it vibrates. Let's examine what each option actually implies about amplitude behaviour.

1. Free vibration: This term only describes a system oscillating under its own elastic and inertia forces after an initial disturbance, with no continuing external force; it says nothing by itself about whether the amplitude stays constant or decays, since a free vibration can be undamped (constant amplitude) or damped (decaying amplitude), so it is too broad and non-specific to describe the reduction pattern given.
2. Forced vibration: This describes a system driven by a continuously applied external periodic force; in steady state, its amplitude typically settles to a constant value determined by the forcing, rather than progressively shrinking cycle after cycle, so it does not match a steadily reducing amplitude.
3. Damped vibration: Damping mechanisms, such as friction, air resistance, or a dashpot, continuously dissipate mechanical energy out of the system as heat. Since each cycle removes some of the vibrational energy, the amplitude must decrease progressively from one cycle to the next, exactly as the question describes.
4. Underdamped vibration: This is a more specific sub-case of damped vibration where the damping is light enough that oscillation still occurs (as opposed to overdamped or critically damped, where no oscillation occurs at all); while it does show decaying amplitude, "damped vibration" is the general, correct umbrella term the question is asking for, and the question does not specify the particular sub-case needed to justify choosing this narrower term.

A progressive drop in amplitude cycle after cycle is the defining signature of energy dissipation, which is what damped vibration describes.

Therefore, the correct answer is damped vibration.