Correct Answer - Option 2 :
\(\dfrac{1}{s+2}\)
Concept:
The Laplace transform of a general exponential signal is given by:
\(L[e^{-at}]\longleftrightarrow \frac{1}{s+a}\)
where 'a' is any positive integer.
Calculation:
Given, f (t) = e-2t
The Laplace transform is given as:
F(s) = \(\frac{1}{s+2}\)
Some important Laplace transforms:
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f(t)
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f(s)
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ROC
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1.
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δ(t)
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1
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Entire s-plane
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2.
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e-at u(t)
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\(\frac{1}{{s + a}}\)
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s > - a
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3.
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e-at u(-t)
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\(\frac{1}{{s + a}}\)
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s < - a
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4.
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cos ω0 t u(t)
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\(\frac{s}{{{s^2} + \omega _0^2}}\)
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s > 0
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5.
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te-at u(t)
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\(\frac{1}{{{{\left( {s + a} \right)}^2}}}\)
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s > - a
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6.
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sin ω0t u(t)
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\(\frac{{{\omega _0}}}{{{s^2} + \omega _0^2}}\)
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s > 0
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7.
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u(t)
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1/s
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s > 0
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