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2 cards from this section. Quick, good the night before a test.
Define the Heaviside Step Function.
What happens before and after time c?
State the main statement of the Second Shifting Theorem.
Think about what happens with the function when it’s delayed.
What does the Second Shifting Theorem help in modeling?
Focus on the 'shifting' aspect of the theorem.
True or False: The Heaviside step function must be included for the Second Shifting Theorem to apply.
Recall what the Heaviside function actually does in modeling.
Prove the Second Shifting Theorem by calculating the Laplace transform of f(t) = e^(at)u(t-b).
Introduce a substitution of u(t-b) correctly before integrating.
Determine the Laplace transform for f(t) = sin(ω(t-5))u(t-5).
Standardize to sin(ωt) first before incorporating the delay.
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