Which damping case yields a non-oscillatory response that reaches the final value fastest?

• A. Underdamped
• B. Overdamped
• C. Critically Damped
• D. Undamped

Answer: (C)

The key idea is how damping changes the transient path to the final value. If damping is too low, the system oscillates and never settles cleanly to the final value. If damping is high, the response is non-oscillatory but slow, because both decay paths fight each other and one dominates, making the approach to the final value take longer. When damping is just right—critically damped—the system returns to the final value as quickly as possible without overshooting. That makes it the fastest non-oscillatory response. In contrast, the overdamped case is non-oscillatory but slower, and the underdamped case produces oscillations, so neither matches the requirement of non-oscillatory and fastest.