12.4.2. Scaling Property

Try these first

1. 1.

   What is the scaling property of the Dirac delta function?

   Hint

   Think about how the argument affects both the delta function's shape and height.

2. 2.

   If δ(x) has an area of 1, what happens when you scale it to δ(3x)?

   Hint

   Remember the area under the curve for the delta function should always be constant.

3. 3.

   What does the scaling property state for the delta function?

   • A) δ(ax) = aδ(x)
   • B) δ(ax) = (1/a)δ(x)
   • C) δ(ax) = (1/|a|)δ(x)

   Hint

   Focus on correlating the changes to the function's amplitude.

4. 4.

   True or False: Scaling a delta function changes its area.

   • True
   • False

   Hint

   Consider the fundamental properties of the delta function.

5. 5.

   A concentrated load at δ(x) is scaled by a factor of 2 (i.e., δ(2x)). How would this scaling affect the load's representation, and what would the new amplitude be?

   Hint

   Revisit the scaling property formula to check the relationship.

6. 6.

   Given δ(-3x) = ? How does scaling and the negative affect the function’s properties?

   Hint

   Remember to consider what the absolute value means for the scaling.