12.2.2. Gaussian Approximation

Try these first

1. 1.

   What is the defining property of the Dirac delta function?

   Hint

   Consider its behavior across a number line.

2. 2.

   What does the term 'Gaussian' refer to in Gaussian approximation?

   Hint

   Think of the graph of the function.

3. 3.

   What is the effect of reducing ϵ in the Gaussian approximation?

   • The area increases
   • The area stays the same
   • The area decreases

   Hint

   Remember the defining property of the delta function.

4. 4.

   True or False: The Gaussian approximation is the same as the Dirac delta function.

   • True
   • False

   Hint

   Consider the limits of each function.

5. 5.

   Discuss the limitations of using the Gaussian approximation in the case of sudden impact loads in structural systems.

   Hint

   What are the sustaining forces in an actual impact scenario?

6. 6.

   If a Gaussian function has a standard deviation of 1, how would you adjust it to better approximate a delta function?

   Hint

   Focus on the properties of Gaussian functions and delta approximation.