Question

What will be the Laplace transform for f(t) = e^-bt u(t) ?
1. \(F(s)= \frac{s}{s+b}\)
2. \(F(s)= \frac{1}{s(s+b)}\)
3. \(F(s)= \frac{1}{s+b}\)
4. \(F(s)= \frac{s}{1+b}\)

Answer 1

Correct Answer - Option 3 : \(F(s)= \frac{1}{s+b}\)

Concept:

The Laplace transform of a general exponential signal is given by:

\(L[e^{-bt}]\longleftrightarrow \frac{1}{s+b}\)

where 'a' is any positive integer.

Some important Laplace transforms:

	f(t)	f(s)	ROC
1.	δ(t)	1	Entire s-plane
2.	e-at u(t)	\(\frac{1}{{s + a}}\)	s > - a
3.	e-at u(-t)	\(\frac{1}{{s + a}}\)	s < - a
4.	cos ω0 t u(t)	\(\frac{s}{{{s^2} + \omega _0^2}}\)	s > 0
5.	te-at u(t)	\(\frac{1}{{{{\left( {s + a} \right)}^2}}}\)	s > - a
6.	sin ω0t u(t)	\(\frac{{{\omega _0}}}{{{s^2} + \omega _0^2}}\)	s > 0
7.	u(t)	1/s	s > 0