Determine the transfer function (H(s)) of the following system using Laplace transform properties. ddot{{y}}+{4}dot{{y}}+{4}{y}=-{x}+{2}dot{{x}} Note: Assume that all initial conditions are zero

postillan4 2021-01-10 Answered
Determine the transfer function (H(s)) of the following system using Laplace transform properties.
y¨+4y˙+4y=x+2x˙
Note: Assume that all initial conditions are zero
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Expert Answer

Brittany Patton
Answered 2021-01-11 Author has 100 answers
Step 1
According to the given information, it is required to determine the transfer function H(s) using Laplace transform properties.y¨+4y˙+4y=x+2x˙
Step 2
Now represent the above differential equation in transfer function form. It is also given that initial conditions are zero.
y¨+4y˙+4y=x+2x˙
L(y¨+4y˙+4y)=L(x+2x˙)
s2Y(s)sY(0)y(0)+4[sY(s)y(0)]+4Y(s)=X(s)+2[sX(s)x(0)]
since initial conditions are all 0:
s2Y(s)+4sY(s)+4Y(s)=X(s)+2sX(s)
(s2+4s+4)Y(s)=(1+2s)X(s)
H(s)=Y(s)H(s)=1+2ss2+4s+4
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