Problem. Transfer function. Inverse Laplace with distinct and repeated poles. IVT and F A system with input x and output y is characterized by the differential equation: ÿ+ ÿ = x Y(s) a) Obtain the system transfer function H(s)= %3D X (s) b) Obtain the system impulse response h(t). Verify the values h(0* ) and h() by using the Initial Value Theorem (IVT) and the Final Value Theorem (FVT). c) Obtain the system step response by two different approaches: 1) Using the TF and PFE with repeated poles. 2) By integrating the impulse response. Why would approach 2) work?
Problem. Transfer function. Inverse Laplace with distinct and repeated poles. IVT and F A system with input x and output y is characterized by the differential equation: ÿ+ ÿ = x Y(s) a) Obtain the system transfer function H(s)= %3D X (s) b) Obtain the system impulse response h(t). Verify the values h(0* ) and h() by using the Initial Value Theorem (IVT) and the Final Value Theorem (FVT). c) Obtain the system step response by two different approaches: 1) Using the TF and PFE with repeated poles. 2) By integrating the impulse response. Why would approach 2) work?
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![Problem. Transfer function. Inverse Laplace with distinct and repeated poles. IVT and FVT
A system with input x and output y is characterized by the differential equation:
j+ ÿ = x
Y(s)
a) Obtain the system transfer function H(s)=
X (s)
b) Obtain the system impulse response h(t). Verify the values h(0* ) and h(0) by
using the Initial Value Theorem (IVT) and the Final Value Theorem (FVT).
c) Obtain the system step response by two different approaches:
1) Using the TF and PFE with repeated poles.
2) By integrating the impulse response. Why would approach 2) work?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffb9a7c18-65f1-48ed-bb7e-4937a04e4157%2F4f190ef7-2c2f-406b-ab46-48ce330a9cab%2Fqtjwq6g_processed.png&w=3840&q=75)
Transcribed Image Text:Problem. Transfer function. Inverse Laplace with distinct and repeated poles. IVT and FVT
A system with input x and output y is characterized by the differential equation:
j+ ÿ = x
Y(s)
a) Obtain the system transfer function H(s)=
X (s)
b) Obtain the system impulse response h(t). Verify the values h(0* ) and h(0) by
using the Initial Value Theorem (IVT) and the Final Value Theorem (FVT).
c) Obtain the system step response by two different approaches:
1) Using the TF and PFE with repeated poles.
2) By integrating the impulse response. Why would approach 2) work?
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