- #1
Spoolx
- 38
- 0
Homework Statement
f(s) = 6/s^2-9
Homework Equations
I think
f(t) = (1/b-a)(e^-at-e^-bt)
The Attempt at a Solution
Replace 6/s^2-9 with 6/(s-3)(s+3)
a=-3
b=3
Plug in
(1(6)/3-(-3))(e^-(-3)t-e^-3t)
Final Result
e^3t-e^-3t
Spoolx said:Homework Statement
f(s) = 6/s^2-9
Homework Equations
I think
f(t) = (1/b-a)(e^-at-e^-bt)
The Attempt at a Solution
Replace 6/s^2-9 with 6/(s-3)(s+3)
a=-3
b=3
Plug in
(1(6)/3-(-3))(e^-(-3)t-e^-3t)
Final Result
e^3t-e^-3t
The purpose of solving this problem is to find the original function from its Laplace transform. This can be useful in many areas of science and engineering, such as solving differential equations and analyzing circuit systems.
To solve this problem, you will need the Laplace transform of the function in question, as well as any other known information about the function, such as initial conditions or constants.
The general process for solving this problem involves using techniques such as partial fractions, completing the square, and inverse Laplace transform tables to manipulate the given function and find the original function.
Some common challenges when solving this problem include determining the correct techniques to use, dealing with complex numbers, and finding the inverse Laplace transform of more complicated functions.
This problem is closely related to other mathematical concepts such as integration, differential equations, and complex analysis. It also has applications in areas such as signal processing and control theory.