Damping in vibrations: The ratio of the actual damping coefficient c to the critical damping coefficient c<sub>c</sub> is termed what, and is the statement ‘‘This ratio is called the damping factor’’ correct?

Difficulty: Easy

Correct Answer: Yes

Explanation:


Introduction / Context

In single-degree-of-freedom vibration systems, characterizing how strongly the system is damped is essential for predicting overshoot, settling time, and resonance behavior. A common nondimensional measure is the ratio of actual damping to critical damping.


Given Data / Assumptions

  • Linear viscous damping model with damping coefficient c.
  • Critical damping coefficient cc = 2mωn (where ωn = √(k/m)).
  • Standard mechanical vibration terminology.


Concept / Approach

The nondimensional ratio ζ = c / cc is called the damping factor or damping ratio. It partitions regimes: ζ < 1 (underdamped), ζ = 1 (critically damped), ζ > 1 (overdamped). This parameter directly enters transmissibility, phase angle, and time-response formulas.


Step-by-Step Solution

1) Define ωn = √(k/m); critical damping cc = 2mωn.2) Form ζ = c / cc.3) Recognize ζ as the damping factor used in standard solutions for free and forced vibrations.


Verification / Alternative check

Time response x(t) for underdamped systems includes e−ζωn t; transmissibility and phase formulas use ζ explicitly, confirming its canonical status.


Why Other Options Are Wrong

  • No: contradicts standard terminology.
  • Only in electrical analogies: ζ is universal across analogous domains (mechanical, electrical RLC).
  • Only for logarithmic decrement: log decrement δ relates to ζ but is not the same quantity.
  • True only for Coulomb friction: ζ pertains to viscous damping models, not dry friction.


Common Pitfalls

  • Interchanging ζ with the percentage of critical damping (which is simply 100ζ%).
  • Confusing damping ratio with damping factor vs. damping coefficient c (dimensional).


Final Answer

Yes

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