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The impulse response of a second order under damped system starting from rest is given by
C(t) = 12.5e-8tcos 6t
What are the responsive value of natural frequency and damping ratio of the system?
- a)10 & 0.6
- b)10 & 0.8
- c)8 & 0.6
- d)8 & 0.8
Correct answer is option 'B'. Can you explain this answer?
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The impulse response of a second order under damped system starting f...
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The impulse response of a second order under damped system starting f...
To find the natural frequency and damping ratio of the system, we need to analyze the given impulse response.
The general form of the impulse response for a second-order underdamped system is given by:
C(t) = A * e^(-ζωnt) * cos(ωdt)
Where:
- A is the amplitude of the response.
- ζ is the damping ratio.
- ωn is the natural frequency.
- ωd is the damped frequency.
Comparing the given impulse response C(t) = 12.5e^(-8t) * cos(6t) with the general form, we can see that:
- A = 12.5
- ζ = 8
- ωn = 6
Therefore, the responsive value of the natural frequency is 6 and the damping ratio is 8.
The general form of the impulse response for a second-order underdamped system is given by:
C(t) = A * e^(-ζωnt) * cos(ωdt)
Where:
- A is the amplitude of the response.
- ζ is the damping ratio.
- ωn is the natural frequency.
- ωd is the damped frequency.
Comparing the given impulse response C(t) = 12.5e^(-8t) * cos(6t) with the general form, we can see that:
- A = 12.5
- ζ = 8
- ωn = 6
Therefore, the responsive value of the natural frequency is 6 and the damping ratio is 8.
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The impulse response of a second order under damped system starting from rest is given byC(t) = 12.5e-8tcos 6tWhat are the responsive value of natural frequency and damping ratio of the system?a)10 & 0.6b)10 & 0.8c)8 & 0.6d)8 & 0.8Correct answer is option 'B'. Can you explain this answer?
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