Practice Definition and Derivation of H(s): The Input-Output Ratio - 5.5.1 | Module 5: Laplace Transform Analysis of Continuous-Time Systems | Signals and Systems
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5.5.1 - Definition and Derivation of H(s): The Input-Output Ratio

Learning

Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

What does H(s) represent in system analysis?

πŸ’‘ Hint: Think about the relationship between input and output in simpler terms.

Question 2

Easy

What is assumed under zero initial conditions?

πŸ’‘ Hint: Consider how initial conditions affect system behavior.

Practice 4 more questions and get performance evaluation

Interactive Quizzes

Engage in quick quizzes to reinforce what you've learned and check your comprehension.

Question 1

What does H(s) indicate in an LTI system?

  • A measure of energy
  • The input-output relationship
  • The time domain signal

πŸ’‘ Hint: Think about how inputs and outputs interact.

Question 2

True or False: H(s) can be used without considering initial conditions.

  • True
  • False

πŸ’‘ Hint: Reflect on what assuming zero initial conditions implies.

Solve 1 more question and get performance evaluation

Challenge Problems

Push your limits with challenges.

Question 1

Given the LCCDE: 2y'' + 3y' + y = 1x, derive H(s). Discuss what each component contributes to the system response.

πŸ’‘ Hint: Break down the equation part by part during transformation.

Question 2

If a system has poles at s = -2 and s = -1, determine its stability and general behavior based on H(s).

πŸ’‘ Hint: Remember how poles indicate stability based on their real components.

Challenge and get performance evaluation