Quiz on Laplace Transforms
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1. What is `2 y(t)` in Laplace domain?
A. `2 \delta(t)`
- Incorrect. The impulse function `2 \delta(t)` is from the inverse Laplace transform of the number 2
B. `2 Y(s)`
- Correct. The Laplace transform of a time domain variable `y(t)` is the same variable but in the Laplace domain `Y(s)`.
C. `Y(s) y(t)`
- Incorrect. Laplace domain (s) and time domain (t) functions never appear together
D. `Y(s)^2`
- Incorrect. The conversion to Laplace domain is not integration
2. What is the Laplace transform of `{d^2f}/{dt^2}` with f(0) = 1 and f'(0) = 2?
A. `s^2F(s) - 2s -1`
- Incorrect. The solution is `s^2 F(s) - s f(0) - f'(0)`
B. `2sF(s) - 2s -2`
- Incorrect. The solution is `s^2 F(s) - s f(0) - f'(0)`
C. `s^2F(s) - s -2`
- Correct. The solution is `s^2 F(s) - s f(0) - f'(0)`
D. `s^2F(s) - s + 2`
- Incorrect. The sign before the f'(0) should be negative
3. What is the initial and final value of Y(s) = `{(s + 3)}/{s(2s + 5)(3s + 6)}`?
A. Initial: 1, Final: 1/10
- Incorrect. Use IVT: `y_0 = \lim_{s \to \infty} s Y(s)` and FVT: `y_\infty = \lim_{s \to 0} s Y(s)`
B. Initial: 1, Final: 0
- Incorrect. Use IVT: `y_0 = \lim_{s \to \infty} s Y(s)` and FVT: `y_\infty = \lim_{s \to 0} s Y(s)`
C. Initial: 0, Final: 1
- Incorrect. Use IVT: `y_0 = \lim_{s \to \infty} s Y(s)` and FVT: `y_\infty = \lim_{s \to 0} s Y(s)`
D. Initial: 0, Final: 1/10
- Correct.IVT: `y_0 = \lim_{s \to \infty} s Y(s)= (\infty+3) / {(2*\infty+5)(3*\infty+6)} = 0`FVT: `y_\infty = \lim_{s \to 0} s Y(s) = 3/{(5)(6)} = 1/{10}`
