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The roots of the characteristic equation of the second order system in which real and imaginary part represents the :
- a)Damped frequency and damping
- b)Damping and damped frequency
- c)Natural frequency and damping ratio
- d)Damping ratio and natural frequency
Correct answer is option 'B'. Can you explain this answer?
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The roots of the characteristic equation of the second order system in...
Answer: b
Explanation: Real part represents the damping and imaginary part damped frequency.
Explanation: Real part represents the damping and imaginary part damped frequency.
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The roots of the characteristic equation of the second order system in...
Explanation:
In a second-order system, the characteristic equation is given by:
s^2 + 2ζω_ns + ω_n^2 = 0
where s is the complex variable, ω_n is the natural frequency, and ζ is the damping ratio.
Damping and Damped Frequency:
The damping ratio (ζ) represents the amount of damping in the system, while the damped frequency (ω_d) represents the frequency of the oscillations in the system. The damping ratio determines whether the system is underdamped (0 < ζ="" />< 1),="" critically="" damped="" (ζ="1)," or="" overdamped="" (ζ="" /> 1).
Natural Frequency and Damping Ratio:
The natural frequency (ω_n) represents the frequency at which the system would oscillate if there was no damping present. It is solely determined by the system's physical properties such as mass and stiffness. The damping ratio (ζ) represents the amount of damping in the system.
Relationship between the Roots and the System Parameters:
The roots of the characteristic equation can be found by solving the quadratic equation. The roots can be real or complex conjugate depending on the values of ω_n and ζ.
If the roots are real, they represent the damping in the system. The real part of the roots represents the damping (ζ), while the imaginary part represents the damped frequency (ω_d).
If the roots are complex conjugate, they represent the oscillatory behavior of the system. The real part of the roots represents the damping ratio (ζ), while the imaginary part represents the damped frequency (ω_d).
Therefore, the correct answer is option 'B' which states that the roots of the characteristic equation represent the damping and damped frequency.
In a second-order system, the characteristic equation is given by:
s^2 + 2ζω_ns + ω_n^2 = 0
where s is the complex variable, ω_n is the natural frequency, and ζ is the damping ratio.
Damping and Damped Frequency:
The damping ratio (ζ) represents the amount of damping in the system, while the damped frequency (ω_d) represents the frequency of the oscillations in the system. The damping ratio determines whether the system is underdamped (0 < ζ="" />< 1),="" critically="" damped="" (ζ="1)," or="" overdamped="" (ζ="" /> 1).
Natural Frequency and Damping Ratio:
The natural frequency (ω_n) represents the frequency at which the system would oscillate if there was no damping present. It is solely determined by the system's physical properties such as mass and stiffness. The damping ratio (ζ) represents the amount of damping in the system.
Relationship between the Roots and the System Parameters:
The roots of the characteristic equation can be found by solving the quadratic equation. The roots can be real or complex conjugate depending on the values of ω_n and ζ.
If the roots are real, they represent the damping in the system. The real part of the roots represents the damping (ζ), while the imaginary part represents the damped frequency (ω_d).
If the roots are complex conjugate, they represent the oscillatory behavior of the system. The real part of the roots represents the damping ratio (ζ), while the imaginary part represents the damped frequency (ω_d).
Therefore, the correct answer is option 'B' which states that the roots of the characteristic equation represent the damping and damped frequency.
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The roots of the characteristic equation of the second order system in which real and imaginary part represents the :a)Damped frequency and dampingb)Damping and damped frequencyc)Natural frequency and damping ratiod)Damping ratio and natural frequencyCorrect answer is option 'B'. Can you explain this answer?
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