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What is the time period of a damped oscillator with a damping ratio of 0.1 and a

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Question: What is the time period of a damped oscillator with a damping ratio of 0.1 and a natural frequency of 10 rad/s?

Options:

  1. 0.2 s
  2. 0.3 s
  3. 0.4 s
  4. 0.5 s

Correct Answer: 0.4 s

Solution: 

Time period (T) = 2π/ω_n = 2π/10 = 0.2π ≈ 0.628 s.

What is the time period of a damped oscillator with a damping ratio of 0.1 and a

Practice Questions

Q1
What is the time period of a damped oscillator with a damping ratio of 0.1 and a natural frequency of 10 rad/s?
  1. 0.2 s
  2. 0.3 s
  3. 0.4 s
  4. 0.5 s

Questions & Step-by-Step Solutions

What is the time period of a damped oscillator with a damping ratio of 0.1 and a natural frequency of 10 rad/s?
  • Step 1: Identify the natural frequency (ω_n) given in the problem. Here, ω_n = 10 rad/s.
  • Step 2: Use the formula for the time period (T) of a damped oscillator, which is T = 2π/ω_n.
  • Step 3: Substitute the value of ω_n into the formula: T = 2π/10.
  • Step 4: Simplify the equation: T = 0.2π.
  • Step 5: Calculate the numerical value of T: T ≈ 0.628 seconds.
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