Practice Scaling Property (12.4.2) - Dirac Delta Function - Mathematics (Civil Engineering -1)

Practice: Scaling Property

Lesson 12.4.2Dirac Delta Function

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8 questions

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6 sample questions

Question 1.
What is the scaling property of the Dirac delta function?
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Think about how the argument affects both the delta function's shape and height.
Question 2.
If δ(x) has an area of 1, what happens when you scale it to δ(3x)?
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Remember the area under the curve for the delta function should always be constant.
3Question 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)
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Focus on correlating the changes to the function's amplitude.
4Question 4.
True or False: Scaling a delta function changes its area.
- True
- False
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Consider the fundamental properties of the delta function.
Question 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?
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Revisit the scaling property formula to check the relationship.
Question 6.
Given δ(-3x) = ? How does scaling and the negative affect the function’s properties?
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Remember to consider what the absolute value means for the scaling.

4 more questions in this section. Enroll free to practise them all.