Inverse laplace transform

Therefore, the solution for the current flowing in an RLC circuit with an impulse voltage input and zero initial conditions is I(t) = (1/1.2)e^(-10t). In summary, the equation for the current flowing in an RLC circuit with an impulse voltage input and zero initial conditions is I(t) = (1/1.2)e^(-10t).
  • #1
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Homework Statement



Derive an equation to represent the current flowing in an RLC circuit where R=12 L=1.2 C=30microfrards with an impulse voltage input. Assume zero conditions when the switch is closed.

Homework Equations





The Attempt at a Solution


I have used the voltage to equal 1, laplace transformed the RLC values and started from basic Kirschoffs law to give
I= s/(1.2s^2+12s)+1

To complete this I know I need to inverse laplace it but cannot get this equation into a format to do it. Can anyone please help before I pull my hair out how to do this??
 
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  • #2
1/(1.2s + 12) = (1/1.2) / (s+12/1.2) is of the form a / (s+b) which can be found on any standard table of inverse laplace transforms.

The inverse laplace transform of 1 is the dirac delta function.
 

What is the inverse Laplace transform?

The inverse Laplace transform is a mathematical operation that takes a function in the Laplace domain and converts it back to the original function in the time domain.

Why is the inverse Laplace transform important in science?

The inverse Laplace transform is important in science because it allows us to analyze and understand complex functions and systems in the time domain, which is essential for many scientific applications.

How is the inverse Laplace transform calculated?

The inverse Laplace transform can be calculated using various methods, such as partial fraction decomposition, contour integration, or using tables of Laplace transforms. The method used depends on the complexity of the function being transformed.

What types of functions can be transformed using the inverse Laplace transform?

The inverse Laplace transform can be applied to a wide range of functions, including exponential, trigonometric, and polynomial functions, as well as more complex functions such as step functions and impulse functions.

What are some real-world applications of the inverse Laplace transform?

The inverse Laplace transform has various applications in fields such as engineering, physics, and economics. It is used to analyze systems in control theory, study circuits in electrical engineering, and model physical phenomena such as heat transfer and wave propagation.

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