11.4.1. Fourier Cosine Transform

Try these first

1. 1.

   What is the expression for the Fourier Cosine Transform?

   Hint

   Refer to the definition provided in class.

2. 2.

   What is the range of t for the Fourier Cosine Transform?

   Hint

   Think about the domain of functions for this transform.

3. 3.

   What does the Fourier Cosine Transform specifically analyze?

   • Functions on [0
   • ∞)
   • Periodic Functions Only
   • Functions on (−∞
   • ∞)

   Hint

   Think about the limitation of the FCT.

4. 4.

   True or False: The Fourier Cosine Transform allows the analysis of frequency components of functions defined for negative t.

   • True
   • False

   Hint

   Consider the definition of the Fourier Cosine Transform.

5. 5.

   Given a function f(t) = e^(-at)u(t), derive its Fourier Cosine Transform F_c(ω).

   Hint

   Use integration by parts or refer to standard integral tables.

6. 6.

   Analyze how the application of FCT in vibration analysis can impact design decisions for bridges.

   Hint

   Consider historical cases of bridge failures related to vibrations.