9.1.5.1 - Linearity
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Practice Questions
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What is the definition of the unit step function?
💡 Hint: Think about how it models sudden changes.
What is the Laplace Transform of \( u(t) \)?
💡 Hint: Remember it's the transform of the basic unit step function.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is the Laplace Transform of \( u(t-a) \)?
💡 Hint: Focus on how the step function impacts transformation.
True or False: The unit step function is always equal to 1.
💡 Hint: Recall the conditions for the unit step function.
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Challenge Problems
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Consider a mechanical system where a force is applied at t=2 seconds. Model the system using the unit step function and derive the Laplace Transform of the applied force.
💡 Hint: Think about the timing and impact of the function before and after the shift.
For the piecewise function defined as \( f(t) = t \cdot u(t-1) + 2 \cdot u(t-2) \), calculate its Laplace Transform.
💡 Hint: Separate each part according to the shifting theorem.
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