Question

A viscous damping system with free vibrations is said to be critically damped if the damping factor is

• A. Less than one
• B. More than one
• C. One
• D. Zero

Hint:

Critical damping represents the boundary between oscillatory motion and non-oscillatory motion.
This boundary always occurs at a damping ratio of $\zeta = 1$.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
The question asks for the value of the damping factor (damping ratio, \(\zeta\)) that characterizes a critically damped mechanical system.

Step 2: Key Formula or Approach: The damping factor \(\zeta\) is defined as the ratio of the actual damping coefficient \(c\) to the critical damping coefficient \(c_{\text{c}}\):
\[ \zeta = \frac{c}{c_{\text{c}}} \]

Step 3: Detailed Explanation:

• Viscous damping systems are categorized into four types based on the damping factor:

• Under-damped system (\(\zeta < 1\)): The system oscillates with a progressively decaying amplitude.

• Critically damped system (\(\zeta = 1\)): The system returns to its equilibrium position in the shortest possible time without oscillating.

• Over-damped system (\(\zeta > 1\)): The system returns to equilibrium slowly without oscillating.

• Undamped system (\(\zeta = 0\)): The system oscillates continuously with constant amplitude.

Step 4: Final Answer:
The damping factor for a critically damped system is exactly one.