Practice Particular Solution (Forced Response - y_p(t)): The System's Reaction to Specific Input - 2.2.1.3 | Module 2: Time Domain Analysis of Continuous-Time Systems | Signals and Systems
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Knowledge

2.2.1.3 - Particular Solution (Forced Response - y_p(t)): The System's Reaction to Specific Input

Learning

Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

What is the form of the particular solution if the input is a constant K?

💡 Hint: Recall the basic structure of forced responses.

Question 2

Easy

What assumption do you make for the particular solution with input K * e^(alpha * t)?

💡 Hint: Think about how we deal with exponential inputs.

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 is the form of the particular solution if the input is a sinusoidal function?

  • y_p(t) = A * e^(alpha * t)
  • y_p(t) = A * cos(omega * t) + B * sin(omega * t)
  • y_p(t) = A

💡 Hint: Think about how sinusoidal responses are structured.

Question 2

True or False: The particular solution can be constant when the input is a polynomial.

  • True
  • False

💡 Hint: Recall how polynomial inputs shape our solutions.

Solve and get performance evaluation

Challenge Problems

Push your limits with challenges.

Question 1

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.

Question 2

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.

Challenge and get performance evaluation