Practice Special Case: Δ(t) (10.2) - The Dirac Delta Function (Impulse Function)

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6 sample questions

Question 1.
What is the value of δ(t−2) when t = 3?
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Evaluate the condition where t does not equal 2.
Question 2.
What is the integral of δ(t−1) from -∞ to +∞?
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Recall the defining property of the Dirac Delta Function.
3Question 3.
What is the value of δ(t) when t = 0?
- 0
- ∞
- 1
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Think about the definition of the Dirac Delta Function.
4Question 4.
The Laplace Transform of δ(t−a) is equal to:
- e^(-as)
- 1
- k * e^(-as)
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Recall the formula we derived.
Question 5.
Given the equation d^2y/dt^2 + 3dy/dt + 2y = δ(t−2), solve for y(t) and provide the solution using Laplace Transforms.
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Break it down with impulse response considerations.
Question 6.
A system is defined with L(s) = (2s + 3)/(s^2 + 5s + 6). How does this equation behave when an impulse input δ(t) is applied at multiple points?
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Make sure to evaluate at each impulse point.

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