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What is the time period of a damped oscillator with a damping ratio of 0.1 and a
What is the time period of a damped oscillator with a damping ratio of 0.1 and a natural frequency of 10 rad/s?
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What is the time period of a damped oscillator with a damping ratio of 0.1 and a natural frequency of 10 rad/s?
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Time period (T) = 2π/ω_n = 2π/10 = 0.2π ≈ 0.628 s.
Questions & Step-by-step Solutions
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Q
Q: What is the time period of a damped oscillator with a damping ratio of 0.1 and a natural frequency of 10 rad/s?
Solution:
Time period (T) = 2π/ω_n = 2π/10 = 0.2π ≈ 0.628 s.
Steps: 5
Show Steps
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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