Practice Natural Response (2.2.2.1) - Time Domain Analysis of Continuous-Time Systems
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Natural Response

Practice - Natural Response

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Practice Questions

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Question 1 Easy

What is the definition of natural response in LTI systems?

💡 Hint: Think about how systems react without external force.

Question 2 Easy

What is the homogeneous solution?

💡 Hint: Consider what happens in a system in isolation.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What describes the natural response of a system?

It's the response due to input.
It doesn't depend on the initial conditions.
It's the response due to initial conditions only.

💡 Hint: Recall the scenario with zero input.

Question 2

Is the transient response permanent?

True
False

💡 Hint: Think about how things settle in a system.

1 more question available

Challenge Problems

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Challenge 1 Hard

Given a second-order LTI system with differential equation d^2y/dt^2 + 3dy/dt + 2y = 0, derive the natural response assuming initial conditions y(0)=1 and y'(0)=0.

💡 Hint: Remember to plug in initial conditions into your derived expression.

Challenge 2 Hard

For a given LTI system with a characteristic equation yielding complex roots, describe the resulting transient response.

💡 Hint: Relate the behavior of complex roots to oscillation and stability.

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Reference links

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