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What is the time period of a damped oscillator with a natural frequency of 3 rad

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Question: What is the time period of a damped oscillator with a natural frequency of 3 rad/s and a damping ratio of 0.1?

Options:

  1. 2π/3
  2. 2π/3.1
  3. 2π/3.2
  4. 2π/3.3

Correct Answer: 2π/3

Solution: 

Time period (T) = 2π/ω_n = 2π/3 rad/s = 2π/3.

What is the time period of a damped oscillator with a natural frequency of 3 rad

Practice Questions

Q1
What is the time period of a damped oscillator with a natural frequency of 3 rad/s and a damping ratio of 0.1?
  1. 2π/3
  2. 2π/3.1
  3. 2π/3.2
  4. 2π/3.3

Questions & Step-by-Step Solutions

What is the time period of a damped oscillator with a natural frequency of 3 rad/s and a damping ratio of 0.1?
  • Step 1: Identify the natural frequency (ω_n) of the damped oscillator. In this case, it is given as 3 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/3 rad/s.
  • Step 4: Calculate the time period T, which is equal to 2π/3.
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