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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is the value of the unit step function \( u(t-2) \) at \( t=1 \)?
💡 Hint: Remember that it equals 0 for times less than 'a'.
Question 2
Easy
State the general Laplace Transform formula for the unit step function.
💡 Hint: Think about what parts relate to the shift and the function itself.
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 value of the unit step function \( u(t-1) \) when \( t < 1 \)?
- 0
- 1
- Undefined
💡 Hint: Think back to the definition of the unit step function.
Question 2
The Laplace Transform of the unit step function \( u(t-a) \) is:
- \\( \\frac{e^{-as}}{s} \\)
- \\( \\frac{e^{as}}{s} \\)
- \\( \\frac{1}{s} \\)
💡 Hint: Use what you've learned about the exponential decay in transformation.
Solve 2 more questions and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Formulate the Laplace Transform for the function \( e^{3t}u(t-2) \) and solve for its inverse.
💡 Hint: Remember to adjust for the value of 'a' in the shifting.
Question 2
Solve \( y'' + 4y = u(t-1) \) using the Laplace transform and find the complete solution.
💡 Hint: Consider the initial conditions you have with this equation.
Challenge and get performance evaluation