Q. The system 2d2y/dt2+4dy/dt+8y=8x, has damping ratio______
a. 0.25
b. 0.1
c. 0.33
d. 0.5
Answer and Explanation
Answer is 0.5
The given System is a second order system and is given by
2d2y/dt2+4dy/dt+8y=8x
After taking the Laplace Transform we get
2s2Y(s)+4sY(s)+8Y(s)=8X(s)
or
(2s2+4s+8) Y(s)=8X(s)
Y(s)/X(s) =8/(2s2+4s+8)
so, the transfer function of the system is
T(s)=Y(s)/X(s) =4/(s2+2s+4)
comparing with a general second Transfer function
T(s)= ωn2 / (s2+2ζωn s+ωn2
ωn2 =4 so ωn=2
2ζωn=2, so ζωn=1 and ζ=1/ωn =1/2=0.5
So the ans is 0.5.
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