What is the time constant of a second-order system with a damping ratio of 0.5 a

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Question: What is the time constant of a second-order system with a damping ratio of 0.5 and natural frequency of 2 rad/s?

Options:

Correct Answer: 1

Solution:

The time constant for a second-order system can be approximated as 1/(damping ratio * natural frequency), which is 1/(0.5 * 2) = 1.

What is the time constant of a second-order system with a damping ratio of 0.5 and natural frequency of 2 rad/s?

What is the time constant of a second-order system with a damping ratio of 0.5 and natural frequency of 2 rad/s?

Step 1: Identify the damping ratio and natural frequency from the question. The damping ratio is 0.5 and the natural frequency is 2 rad/s.
Step 2: Write down the formula for the time constant of a second-order system: time constant = 1 / (damping ratio * natural frequency).
Step 3: Substitute the values into the formula: time constant = 1 / (0.5 * 2).
Step 4: Calculate the product of the damping ratio and natural frequency: 0.5 * 2 = 1.
Step 5: Now, calculate the time constant: time constant = 1 / 1 = 1.

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