Practice - Particular Solution (Forced Response - y_p(t)): The System's Reaction to Specific Input
Practice Questions
Test your understanding with targeted questions
What is the form of the particular solution if the input is a constant K?
💡 Hint: Recall the basic structure of forced responses.
What assumption do you make for the particular solution with input K * e^(alpha * t)?
💡 Hint: Think about how we deal with exponential inputs.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is the form of the particular solution if the input is a sinusoidal function?
💡 Hint: Think about how sinusoidal responses are structured.
True or False: The particular solution can be constant when the input is a polynomial.
💡 Hint: Recall how polynomial inputs shape our solutions.
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Challenge Problems
Push your limits with advanced challenges
A continuous-time LTI system has the homogeneous solution y_h(t) = e^(-2t) * (C1 * cos(3t) + C2 * sin(3t)). If the input is x(t) = 5 * e^(2t), determine the particular solution y_p(t).
💡 Hint: Consider how exponentials impact the system’s behavior.
If the input to an LTI system is x(t) = 4 * cos(5t) + 2 * sin(5t) and the system's frequency matches 5 rad/s, how would you modify your assumed y_p(t)?
💡 Hint: Focus on matching input frequency with characteristics of the homogeneous solution.
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Reference links
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