10.2.3.2 - Scaling
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Practice Questions
Test your understanding with targeted questions
Define scaling in the context of Fourier transforms.
💡 Hint: Think about how a function changes when its argument is modified.
What happens to the Fourier transform of f(ax) if a > 1?
💡 Hint: Recall that scaling can stretch or compress functions.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is the scaling property in Fourier transforms?
💡 Hint: This relates to how we adjust inputs in mathematical transformations.
True or False: Scaling only stretches functions.
💡 Hint: Consider how both high and low values can affect the graph of a function.
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Challenge Problems
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Analyze the effects of scaling on a modeled beam subject to a load that varies with length. Explain the theoretical implications for both short and long beams.
💡 Hint: Consider how material properties influence beam characteristics at different scales.
You have a thermal system modeled with parameters that scale with wall thickness. How would scaling impact the heat diffusion analysis?
💡 Hint: Analyze how thickness alters thermal gradients over time.
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