10.9.2 - Sine Transform of First Derivative
Enroll to start learning
You’ve not yet enrolled in this course. Please enroll for free to listen to audio lessons, classroom podcasts and take practice test.
Practice Questions
Test your understanding with targeted questions
What is the Sine Transform of the first derivative?
💡 Hint: Look for the formula relating f' and f.
Why is the Sine Transform useful in civil engineering?
💡 Hint: Think about the types of problems engineers face.
4 more questions available
Interactive Quizzes
Quick quizzes to reinforce your learning
What does the Sine Transform of the first derivative equate to?
💡 Hint: Remember the boundary term in the transformation.
True or False: The Sine Transform is useful when the function value at one boundary is zero.
💡 Hint: Think about the types of boundary conditions suitable for the Sine Transform.
Get performance evaluation
Challenge Problems
Push your limits with advanced challenges
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.
💡 Hint: Differentiate f(x) first before applying the transform.
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.
💡 Hint: Consider what happens at the fixed end and free end of the beam.
Get performance evaluation
Reference links
Supplementary resources to enhance your learning experience.