(a) Given, F (S) = {3 S^2 - 6 S + 9} / {(S + 1)(S - 2)^2}, find f (t). (b) Given, F(S) = {6 S^2 +...
Question:
(a) Given, {eq}\displaystyle F (S) = \dfrac {3 S^2 - 6 S + 9} {(S + 1)(S - 2)^2} {/eq}, find {eq}f (t) {/eq}.
(b) Given, {eq}\displaystyle F(S) = \dfrac {6 S^2 + 2 S + 42} {(S - 1) (S^2 + 2)^2} {/eq}, find {eq}f (t) {/eq}.
Laplace transform:
Laplace transform is an integral transform which transforms a function of a real variable t to a function of a complex variable s.
The Laplace transform of a function in the time domain {eq}f\left( t \right) {/eq} is given by
{eq}L\left\{ f\left( t \right) \right\} =F\left( s \right) =\int _{ 0 }^{ \infty }{ { e }^{ -st }f\left( t \right) dt } {/eq}
Answer and Explanation: 1
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View this answer(a) Given, {eq}\displaystyle F (S) = \dfrac {3 S^2 - 6 S + 9} {(S + 1)(S - 2)^2} {/eq}
Lets split the fuction into partial fractions
which gives,
...
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Chapter 18 / Lesson 1The Laplace Expansion equation (LEE) applies determinants of smaller matrices to a larger square matrix to identify the determinant. Analyze the LLE method to break down the equation into mathematical operations and apply it to the so-called checkerboard where N = 1, 2, or 3.