What is the Inverse Laplace Transform of (9s+5)/(s2-9) with s>3?

In summary, to find the inverse Laplace Transform of (9s+5)/(s2-9) given s>3, use the table of Laplace Transforms and apply the formula "sinh at" goes with a/(s2-a2) and "cosh at" goes with s/(s2-a2). "cosh" represents the hyperbolic cosine function, which can be expressed as (1/2)(e^x + e^-x). Similarly, "sinh" represents the hyperbolic sine function, which can be expressed as (1/2)(e^x - e^-x).
  • #1
Hogger
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Homework Statement


Find the inverse Laplace Transform of (9s+5)/(s2-9) given s>3


Homework Equations


I have a table of Laplace Transforms.
it says "sinh at" goes with a/(s2-a2) and "cosh at" goes with s/(s2-a2)


The Attempt at a Solution


I know how to split it up and find the inverse Laplace Transform but I don't know what it means by "cosh". I assume it is some variation of cosine? Someone said it means degrees but I don't see how that would change the problem.
 
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  • #2
cosh(x) = 1/2 [exp(x) + exp(-x)]


sinh(x) = 1/2 [exp(x) - exp(-x)]
 
  • #3
thanks, apparently the professor somewhat explained this but I missed it.
 

FAQ: What is the Inverse Laplace Transform of (9s+5)/(s2-9) with s>3?

What is the Laplace Transform?

The Laplace Transform is a mathematical tool used to transform a function from the time domain to the frequency domain. It is particularly useful in solving differential equations and analyzing systems in engineering and physics.

How is the Laplace Transform calculated?

The Laplace Transform is calculated by integrating a function with respect to a complex variable, s. The resulting function is known as the Laplace Transform and is denoted by the symbol L(f(t)).

What is the purpose of using the Laplace Transform?

The Laplace Transform allows us to solve differential equations and analyze systems in the frequency domain, which is often easier and more convenient than the time domain. It also helps us to understand the behavior of a system and its response to different inputs.

Are there any limitations to using the Laplace Transform?

Yes, there are some limitations to using the Laplace Transform. It can only be applied to functions that are defined for all positive time values, and it cannot be used for functions with discontinuities or infinite discontinuities.

How is the Laplace Transform related to the Fourier Transform?

The Laplace Transform is a generalization of the Fourier Transform, which is used to transform a function from the time domain to the frequency domain. The Fourier Transform is a special case of the Laplace Transform, where the complex variable s is equal to jω, where ω is the frequency in radians per second.

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