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4 cards from this section. Quick, good the night before a test.
State the definition of the unit step function.
Think about what happens before and after time a.
What is the Laplace Transform of u(t)?
Recall how the unit step function behaves from a time perspective.
What is the Laplace Transform of u(t-a)?
Recall the definition of the transform.
True or False: The unit step function can only take values 0 or 1.
Think about the properties of the unit step function.
For a function f(t) = sin(t) and a = 2, derive the Laplace Transform of f(t)u(t-2).
Think about the second shifting theorem and how it applies here.
Design a control system using u(t-1) that incorporates a delayed response. What does your Laplace Transform yield?
Consider the implications of your delay in a real system.
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