What is the primary characteristic of a critically damped system?
- AIt oscillates indefinitely without returning to equilibrium.
- BIt returns to equilibrium without oscillating and in the shortest possible time.Correct
- CIt oscillates with decreasing amplitude over time.
- DIt takes longer than an underdamped system to return to equilibrium.
Solution
Concept
Characteristics of critically damped systems
Formula
NONE
Step-by-step solution
1. A critically damped system returns to its equilibrium position without oscillating in the shortest time. Answer: B
Explanation
Critical damping represents the precise threshold between an oscillatory underdamped state and a non-oscillatory overdamped state. In a critically damped system, the displacement returns to the equilibrium position as quickly as possible without overshooting or oscillating. Therefore, option B accurately describes the defining characteristic of critical damping.
Why the other options are wrong
C) Oscillating with decreasing amplitude over time describes an underdamped system. D) A critically damped system returns to equilibrium faster than an overdamped system, not an underdamped system.
Shortcut
Critically damped system returns to equilibrium without oscillating in shortest time.
Common mistake
Confusing critically damped behavior with underdamped behavior and selecting option C.
Correct answer: B) It returns to equilibrium without oscillating and in the shortest possible time.