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3 cards from this section. Quick, good the night before a test.
Find the Laplace Transform of e^(2t) sin(t).
Use the theorem to shift based on the coefficient of the exponent.
What do you change in the Laplace domain when you have e^(at)?
Remember the theorem statement!
What does the First Shifting Theorem allow you to do?
Think about how exponential functions interact with transforms.
True or False: Multiplying a function by e^(3t) shifts to the right in the frequency domain.
Recall the direction of the shift when applying the theorem.
Demonstrate the application of the First Shifting Theorem in solving a second-order differential equation involving e^(3t) sin(2t). Provide the full steps.
Start with the standard transform of sin(2t).
Find the Laplace Transform of e^(-4t) (t² + t) and interpret the results given how the theorem modifies it.
Ensure you manage each component separately and apply the shift afterwards.
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