Laplace Transform Calculator

Laplace Transform Calculator: If you are interested in knowing the concept to find the Laplace Transform of a function, then stay on this page. Here, you can see the easy and simple step by step procedure for calculating the laplace transform.

This Laplace Transform Calculator handy tool is easy to use and shows the steps so that you can learn the topic easily. We are providing the best examples so that you can understand the concept. Make your calculations faster with the help of our free online tool.

Solve Laplace Transform of a Function

We all know that calculating Laplace Transform is a little bit tough when compared with other mathematical operations. Have a look at the detailed step by step procedure that is helpful in solving the Laplace Transform of any kind of equation.

  • Take a fiction or an equation to which you want to perform the operation.
  • Perform the integration operation on the given function.
  • Do all mathematical calculations to the solution.
  • Substitute the values in the obtained equation to get the result.

Standard Form

The standard form to represent the Laplace Transform is

F(s)=L(f(x))= Integration 0 to infinity e^-stf(t)dt

where f(t) is a function

s is the complex number frequency parameter

Example:

Question: What is the Laplace Transform of 3sinh(2t)+3sin(2t)?

Solution:

Let us take the functions f(t), g(t)

f(t)=sinh(2t)

g(t)=sin(2t)

Use the linearity property of Laplace Transform

L[a.f(t)+b.g(t)]=a.L[f(t)]+b.L[g(t)]

L[sinh(2t)]=2/s2-4

Lsin(2t)]=2/s2+4

L[3sinh(2t)+3sin(2t)]=3x2/s2-4+3x2/s2+4

=6/s2-4+6/s2+4=6x{1/s2-4+1/s2+4}

=6x{s2+4+s2-4/s4-16}

=6x{2s2/s4-16}

=12s2/s4-16

The Laplace Transform of 3sinh(2t)+3sin(2t) is 12s2/s4-16.

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Laplace Transform Calculator

Frequently Asked Questions on Laplace Transforms

1. What is the purpose of Laplace Transform?

The purpose of the Laplace Transform is to transform ordinary differential equations into algebraic equations. Like the Fourier transform, it is used for solving the integral equations.


2. What are the applications of the Laplace Transform?

The applications of Laplace Transform are Circuit Analysis, Signal Processing, and Communication Systems.


3. Is Laplace Transform linear?

Yes, Laplace Transform is linear.


4. What is the difference between Laplace and Fourier Transform?

The fourier transform doesn't care about changing the magnitudes of a signal. But the laplace transform cares both changing magnitudes and oscillation parts. Actually, the Fourier Transform is a subset of the Laplace Transform.