Practice Sine Transform Of First Derivative (10.9.2) - Fourier Cosine and Sine Transforms

Practice: Sine Transform of First Derivative

Lesson 10.9.2Fourier Cosine and Sine Transforms

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8 questions

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6 sample questions

Question 1.
What is the Sine Transform of the first derivative?
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Look for the formula relating f' and f.
Question 2.
Why is the Sine Transform useful in civil engineering?
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Think about the types of problems engineers face.
3Question 3.
What does the Sine Transform of the first derivative equate to?
- F {f′(x)} = sF {f(x)} - f(0)
- F {f′(x)} = -sF {f(x)}
- F {f′(x)} = F {f(x)}
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Remember the boundary term in the transformation.
4Question 4.
True or False: The Sine Transform is useful when the function value at one boundary is zero.
- True
- False
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Think about the types of boundary conditions suitable for the Sine Transform.
Question 5.
Consider a material with temperature distributed along its length according to the function f(x) = T_0 e^{-kx}. Use the Sine Transform to find the derivative of temperature concerning the distance x.
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Differentiate f(x) first before applying the transform.
Question 6.
Analyzing a cantilever beam, the deflection can be modeled by f(x). If the load at the end is constant, use the Sine Transform to express the first derivative of the deflection at the free end.
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Consider what happens at the fixed end and free end of the beam.

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