Practice Multiplication By A Function (12.4.4) - Dirac Delta Function - Mathematics (Civil Engineering -1)

Practice: Multiplication by a Function

Lesson 12.4.4Dirac Delta Function

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6 sample questions

Question 1.
What is the result of multiplying $f(x)$ by $\delta(x - a)$ ?
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Think about what the delta function does at point a.
Question 2.
Where does the Dirac delta function have non-zero value?
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Recall the definition of the Dirac delta function.
3Question 3.
What does the multiplication of a function $f(x)$ by $\delta(x-a)$ yield?
- Null function
- f(a) \\delta(x-a)
- f(a)
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Think about the sifting property.
4Question 4.
The Dirac delta function has non-zero values at:
- True
- False
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Recall how the delta function behaves.
Question 5.
You are given a function $f(x) = 2x$ and tasked to evaluate the integral $I = \int_{-5}^{5} f(x) \delta(x - 3) dx$ . Find the value of $I$ .
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Recall how the delta function selects the value from the function.
Question 6.
Consider an impulse function $F(t) = 5 \delta(t - 1)$ . If this force is applied to a mass of 10 kg, what is the instantaneous acceleration?
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Apply Newton’s law of motion considering instantaneous force.

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