## Laplace Transform Calculator

You can use an online Laplace transform calculator with steps to offer the conversion of a real-valued function to a complex-valued function. In engineering and research, the Laplace transformation is used to analyze control systems and electronic devices. The laplace calculator can also be used to solve differential equations using the Laplace transform equation. Continue reading to learn how to find Laplace transforms and more!

## Laplace Transform:

Laplace transformations describe integral transformations in math that convert a real-valued function f (t) to a complex-valued function. This transformation is used to convert normal differential equations into algebraic equations that may be used to solve ordinary differential problems.

A linear differential equation is quite common in practical uses, and it frequently emerges from electrical engineering, physics, and control systems challenges. Apart from that, the Laplace transform calculator can only perform regular Laplace transforms, also known as unilateral Laplace transforms. This is because only one side of the Laplace transform (the ordinary side) is used and the inverse Laplace transform side is not used. A web Integral Calculator, on the other hand, can be used to calculate the integrals of functions concerning variables in concern.

## Formulae used by Laplace Calculator:

$$ F(s) \;=\; \int_0^{+∞} f(t) \;.\; e^{-st} \;.\; dt $$## What Is a Laplace Transform Calculator and How Does It Work?

With the following steps, you can turn actual functions into complex functions using a web Laplace transformation calculator:

### Input:

The following is how to how to input values in laplace calculator with steps:

Step 1: In the input field, type the function, function variable, and transformation variable.

Step 2: To acquire the integral transformation, click the "Calculate" button.

Step 3: The outcome will appear on laplace calculator.

### Output:

The following are the outcomes of the laplace calculator with steps:

- First and foremost, the calculator displays your input as an ordinary differential equation.
- Then, in algebraic form, it displays the answer to the equation.
- It also shows plots of given algebraic functions.

## Solved example:

Solve sin(t).t^{4} by Laplace transformation:

**Solution:**

Input:

$$ L_t \left[ t^4 \; sin(t) \right] (s) $$**Result:**

**Plot**

**Plots**

## Conclusion:

Try this laplace transform calculator with steps to see how a real ordinary differential equation is transformed into a complex algebraic expression. You can certainly perform all of these calculations properly, but it is a difficult and time-consuming operation. As a result, students and professionals can quickly calculate using this Laplace transformation calculator.

### Frequently Asked Questions:

## Q: What is the Laplace Transform's principal purpose?

Answer: The Laplace transform's principal purpose is to convert Ordinary Differential Equations (ODEs) into algebraic variables. This conversion aids in the simple solution of ODEs.

## Q: What are the Most Common Laplace Transform Uses?

Answer: The following are some of the most common uses of the Laplace transform:

- Signal Process
- Derive the circuit
- Integrated Circuit
- Control system

## Q: What is the distinction between the Fourier and the Laplace Transforms?

Answer: The Fourier transform alters the magnitudes of a signal by decomposing a function that is location or time-dependent. The Laplace transform, on the other hand, modifies the magnitude and oscillation portions. The main set of the Fourier Transform is the Laplace Transform.

## Q: What Is the Laplace Transform and Why Is It Important?

Answer: When basic conditions are given, such as zero initial numbers, the Laplace transform can be used to find specific forms of differential problems.