Practice Illustrative and Detailed Examples - 5.4.1.4 | Module 5: Laplace Transform Analysis of Continuous-Time Systems | Signals and Systems
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5.4.1.4 - Illustrative and Detailed Examples

Learning

Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

What is the first step in solving a differential equation with Laplace Transform?

πŸ’‘ Hint: Think about converting the equation into a different domain.

Question 2

Easy

Define initial conditions in the context of differential equations.

πŸ’‘ Hint: Consider what is needed to uniquely solve the equation.

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 the Laplace Transform help simplify?

  • Time domain equations
  • Algebraic equations
  • Complex differential equations

πŸ’‘ Hint: Recall its primary function in engineering.

Question 2

True or False: Initial conditions are ignored in Laplace Transform.

  • True
  • False

πŸ’‘ Hint: Think about how we define states at t=0.

Solve and get performance evaluation

Challenge Problems

Push your limits with challenges.

Question 1

A second-order mechanical system is described by the differential equation: md^2x/dt^2 + bdx/dt + kx = f(t), with m = 2kg, b = 3Ns/m, k = 5N/m and with initial conditions x(0)=0, dx/dt(0)=0. Apply the Laplace Transform to derive the output response x(t) when f(t) = 10u(t).

πŸ’‘ Hint: Consider the coefficients and transformations step-by-step carefully.

Question 2

An electrical RLC circuit is characterized by the equation Ld^2i/dt^2 + Rdi/dt + (1/C)i = v(t). Given that L=0.5H, R=1Ξ©, and C=0.002F, with initial conditions i(0)=1A, di/dt(0)=0. Find the current response i(t) for a unit step input.

πŸ’‘ Hint: Don’t forget to convert all coefficients to their proper forms in the Laplace domain.

Challenge and get performance evaluation