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The impulse response of a second order under damped system starting from rest is given by C(t) = 12.5e-8tcos6t
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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Most Upvoted Answer
The impulse response of a second order under damped system starting f...
The impulse response of a second order underdamped system can be written as:
C(t) = A * e^(-alpha*t) * cos(w*t)
where A is the amplitude, alpha is the damping ratio, and w is the natural frequency.
Comparing this with the given impulse response:
C(t) = 12.5 * e^(-8t) * cos(6t)
We can see that alpha = 8 and w = 6.
So, the responsive value of the natural frequency is 6 and the damping ratio is 8.
C(t) = A * e^(-alpha*t) * cos(w*t)
where A is the amplitude, alpha is the damping ratio, and w is the natural frequency.
Comparing this with the given impulse response:
C(t) = 12.5 * e^(-8t) * cos(6t)
We can see that alpha = 8 and w = 6.
So, the responsive value of the natural frequency is 6 and the damping ratio is 8.
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Community Answer
The impulse response of a second order under damped system starting f...
C(t) = 12.5e−8tcos6t,t > 0
T.F = L{C(t} = 12.5(s−(−8))/(s−(−8))2+62)
TfF = (12.5s+100)/(s2+16s+100)
Comparing with s2+2ξωn+ωn2
ωn2 = 100→ωn = 10
2ξωn = 16→ξ = 0.8
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