Question

For a standard second-order system, the \(\xi\) value for underdamped response is

• A. \(\xi=1\)
• B. \(\xi>1\)
• C. \(\xi<1\)
• D. \(\xi=0\)

Hint:

For a second-order system, \[ \boxed{ \begin{aligned} 0 \xi=1 &\rightarrow \text{Critically damped} \xi>1 &\rightarrow \text{Overdamped} \end{aligned} } \]

Answer 1

The Correct Option is C

Step 1: Recall the damping ratio classifications. For a standard second-order system: \[ \begin{aligned} \xi &=0 &&\text{: Undamped} 0 \xi&=1 &&\text{: Critically damped} \xi&>1 &&\text{: Overdamped} \end{aligned} \]

Step 2: Identify the condition for an underdamped response. An underdamped system exhibits oscillatory behavior with gradually decreasing amplitude when \[ 0<\xi<1. \] Thus, \[ \boxed{\xi<1} \] is the correct choice. Therefore, \[ \boxed{(C)} \] is the correct answer.