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If the natural frequency of a damped oscillator is 5 rad/s and the damping ratio
If the natural frequency of a damped oscillator is 5 rad/s and the damping ratio is 0.2, what is the damped frequency?
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Practice Questions
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Q1
If the natural frequency of a damped oscillator is 5 rad/s and the damping ratio is 0.2, what is the damped frequency?
4.8 rad/s
5 rad/s
5.2 rad/s
5.5 rad/s
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Damped frequency (ω_d) = ω_n√(1-ζ^2) = 5√(1-0.2^2) = 5√(0.96) ≈ 4.8 rad/s.
Questions & Step-by-step Solutions
1 item
Q
Q: If the natural frequency of a damped oscillator is 5 rad/s and the damping ratio is 0.2, what is the damped frequency?
Solution:
Damped frequency (ω_d) = ω_n√(1-ζ^2) = 5√(1-0.2^2) = 5√(0.96) ≈ 4.8 rad/s.
Steps: 7
Show Steps
Step 1: Identify the natural frequency (ω_n) of the damped oscillator, which is given as 5 rad/s.
Step 2: Identify the damping ratio (ζ), which is given as 0.2.
Step 3: Use the formula for damped frequency (ω_d): ω_d = ω_n * √(1 - ζ^2).
Step 4: Calculate ζ^2: 0.2^2 = 0.04.
Step 5: Calculate (1 - ζ^2): 1 - 0.04 = 0.96.
Step 6: Take the square root of 0.96: √(0.96) ≈ 0.98.
Step 7: Multiply the natural frequency by the square root: ω_d = 5 * 0.98 ≈ 4.8 rad/s.
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