Practice Definition From Input-output Relationship (zero Initial Conditions) (5.5.1.2)
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Definition from Input-Output Relationship (Zero Initial Conditions)

Practice - Definition from Input-Output Relationship (Zero Initial Conditions)

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Practice Questions

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Question 1 Easy

What does the transfer function H(s) represent?

💡 Hint: Think about how a system behaves in response to input.

Question 2 Easy

How do zero initial conditions affect the analysis of H(s)?

💡 Hint: Consider what happens when a system is inactive before input.

1 more question available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What is the formula for the transfer function H(s)?

H(s) = Y(s) + X(s)
H(s) = Y(s) / X(s)
H(s) = Y(s) - X(s)

💡 Hint: Recall the definition of the transfer function.

Question 2

True or False: The transfer function can be defined without considering initial conditions.

True
False

💡 Hint: Consider what zero initial conditions imply.

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Challenge Problems

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Challenge 1 Hard

Given the differential equation: 2(d^2y/dt^2) + 3(dy/dt) + 1y = 5x(t), derive H(s).

💡 Hint: Apply the Laplace transform considering zero initial conditions.

Challenge 2 Hard

Analyze whether the system H(s) = (s+1)/(s^2+3s+2) is stable. Justify your conclusion.

💡 Hint: Determine where the poles of H(s) lie.

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Reference links

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