Find the laplace of t^3/e^5

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In summary, the Laplace transform is a mathematical operation used to convert functions of time into functions of complex variables. It is commonly used in engineering and physics to solve differential equations and analyze systems in the frequency domain. To find the Laplace transform of a function, one can use a table of common transforms or apply the definition directly. The Laplace transform of t^n is n!/s^(n+1) and the Laplace transform of e^(at) is 1/(s-a). By using the properties of Laplace transform, the transform of t^3/e^5 can be broken down into 3!/s^4 and 1/(s+5), resulting in 6/(s^4(s+5)).
  • #1
angel
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hi,

im trying to find the laplace of t^3/e^5

i get the answer as:

6/e^5.s^4 could someone please confirm this for me.
thanks
 
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  • #2
A casual glance seems to give the expression [tex]\frac{6}{s^{4}e^{5}}[/tex] for the Laplace transform.
However, do use parentheses in the future to make your expressions unambiguous.
 
  • #3


Hi there,

Yes, your answer is correct! The Laplace transform of t^3/e^5 is indeed 6/e^5.s^4. Good job!
 

1. What is the Laplace transform?

The Laplace transform is a mathematical operation that converts a function of time into a function of complex variable s, which represents frequency. It is commonly used in engineering and physics to solve differential equations and analyze systems in the frequency domain.

2. How do you find the Laplace transform of a function?

The Laplace transform of a function f(t) is given by the integral from 0 to infinity of e^(-st)f(t)dt, where s is a complex variable. In order to find the Laplace transform of a specific function, you can use a table of common transforms or apply the definition directly.

3. What is the Laplace transform of t^3?

The Laplace transform of t^3 is 3!/s^4, where n! represents the factorial of n. In general, the Laplace transform of t^n is n!/s^(n+1).

4. What is the Laplace transform of e^5?

The Laplace transform of e^5 is 1/(s-5). In general, the Laplace transform of e^(at) is 1/(s-a).

5. How do you find the Laplace transform of t^3/e^5?

Using the properties of Laplace transform, we can break down this function into t^3 and e^(-5). The Laplace transform of t^3 is 3!/s^4 and the Laplace transform of e^(-5) is 1/(s+5). Therefore, the Laplace transform of t^3/e^5 is 3!/(s^4(s+5)) = 6/(s^4(s+5)).

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