9.1.5.2 - Time-Shift for General Function
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Practice Questions
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What defines the unit step function?
💡 Hint: Think about what happens at the jump point.
Write the Laplace Transform of u(t-a).
💡 Hint: Look for the exponential function in the formula.
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Interactive Quizzes
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What is the unit step function?
💡 Hint: Focus on the defining feature of the function.
True or False: The Laplace Transform is used to convert functions from the frequency domain to time domain.
💡 Hint: Remember the direction of the transform.
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Challenge Problems
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A control system has an input that is turned on at t=3 seconds and remains on indefinitely. Describe how you would model this using the unit step function and derive the Laplace Transform.
💡 Hint: Start by writing down what happens at the time 3 seconds.
You are given a mechanical system that each force is applied suddenly at intervals of 2 seconds. Explain how you would set up the differential equation using the Laplace Transform and the unit step function.
💡 Hint: How does the forces’ sudden application affect the system's motion?
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