Problem 2.149 & 2.150: Response of Damped System Determine the values of 3, wa, and free-vibration response of the following viscously damped systems when x = 0.1 (m), x = 10 (a) m=10 kg, c=150 (b) m=10 kg, c = 200 (c) m=10 kg, c = 250 N • sec m N• sec m N • sec m k = 1,000 k = 1,000 k = 1,000 m N sec m m m
Problem 2.149 & 2.150: Response of Damped System Determine the values of 3, wa, and free-vibration response of the following viscously damped systems when x = 0.1 (m), x = 10 (a) m=10 kg, c=150 (b) m=10 kg, c = 200 (c) m=10 kg, c = 250 N • sec m N• sec m N • sec m k = 1,000 k = 1,000 k = 1,000 m N sec m m m
Elements Of Electromagnetics
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Publisher:Sadiku, Matthew N. O.
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![**Problem 2.149 & 2.150: Response of Damped System**
Determine the values of ζ (damping ratio), ω_d (damped natural frequency), and the free-vibration response of the following viscously damped systems when:
\[ x_0 = 0.1 \, (m), \quad \dot{x}_0 = 10 \, \left(\frac{m}{sec}\right) \]
(a) \( m = 10 \, kg, \quad c = 150 \, \left( \frac{N \cdot sec}{m} \right), \quad k = 1,000 \, \left( \frac{N}{m} \right) \)
(b) \( m = 10 \, kg, \quad c = 200 \, \left( \frac{N \cdot sec}{m} \right), \quad k = 1,000 \, \left( \frac{N}{m} \right) \)
(c) \( m = 10 \, kg, \quad c = 250 \, \left( \frac{N \cdot sec}{m} \right), \quad k = 1,000 \, \left( \frac{N}{m} \right) \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F20000a63-5a8a-4b5e-adbd-85ecbf6c298b%2F58466d5e-0ed7-4aa3-940e-7c4d9e706207%2Fkm97rt5_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem 2.149 & 2.150: Response of Damped System**
Determine the values of ζ (damping ratio), ω_d (damped natural frequency), and the free-vibration response of the following viscously damped systems when:
\[ x_0 = 0.1 \, (m), \quad \dot{x}_0 = 10 \, \left(\frac{m}{sec}\right) \]
(a) \( m = 10 \, kg, \quad c = 150 \, \left( \frac{N \cdot sec}{m} \right), \quad k = 1,000 \, \left( \frac{N}{m} \right) \)
(b) \( m = 10 \, kg, \quad c = 200 \, \left( \frac{N \cdot sec}{m} \right), \quad k = 1,000 \, \left( \frac{N}{m} \right) \)
(c) \( m = 10 \, kg, \quad c = 250 \, \left( \frac{N \cdot sec}{m} \right), \quad k = 1,000 \, \left( \frac{N}{m} \right) \)
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