The Inverse Laplace transform of $\frac{1}{s-2}$ is:
$e^{2t}$
Inverse Laplace Transform Calculation
Understanding the Inverse Laplace Transform
The question asks for the Inverse Laplace transform of the function $f(s) = \frac{1}{s-2}$. The Inverse Laplace transform converts a function in the 's' domain back to the 't' domain, typically representing a time-domain signal.
Standard Laplace Transform Pair
A key pair in Laplace transforms is the transform of an exponential function:
$ L\{e^{at}\} = \frac{1}{s-a} $
Consequently, the corresponding Inverse Laplace transform pair is:
$ L^{-1}\left\{ \frac{1}{s-a} \right\} = e^{at} $
Applying the Formula
We need to find $ L^{-1}\left\{ \frac{1}{s-2} \right\} $.
By comparing the given function $\frac{1}{s-2}$ to the standard form $\frac{1}{s-a}$, we can identify the constant $a$.
In this case, $a = 2$.
Result
Substituting $a=2$ into the Inverse Laplace transform formula $e^{at}$, we get:
$ L^{-1}\left\{ \frac{1}{s-2} \right\} = e^{2t} $
Thus, the Inverse Laplace transform of $\frac{1}{s-2}$ is $e^{2t}$.
Important Questions from Laplace Transform
Which of the following is the final value of the impulse response of the system whose transfer function is
(2s + 1)/(s 4 + 8s 3 + 16s 2 + s)
Find the Laplace transform for the following time domain.
y(t) = -2te -t + 4e -t - 4e -2t
Match List I with List II
List – I
List – II
f(t)
F(S)
A.
e -at
I.
\(\rm \frac{s}{s^2+ \omega^2}\)
B.
te at
II.
\(\rm \frac{\omega}{s^2+ \omega^2}\)
C.
sinωt
III.
\(\rm \frac{1}{(s- a)^2}\)
D.
cosωt
IV.
\(\rm \frac{1}{(s+ a)}\)
Choose the correct answer from the options given below:
The Laplace transform of sin h (at) is
The unilateral Laplace transform of f(t) is \(\frac{1}{s^2+s+1}\). The unilateral Laplace transform of t f(t) is
