4. Inverse laplace_upload

4. Inverse laplace_upload - Inverse Laplace Transform JIN...

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Inverse Laplace Transform JIN KANG
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Definition Like Laplace transform, we can use the integral to solve for f(t) Often F(s) from diff eq is complex Integral method is very difficult Use charts instead to transform F(s) f(t) Transforms Some functions are easily convertible to f(t) through simple use of tables Some functions are not readily pulled from tables solved using partial fraction expansion to reduce polynomials into simple terms [ ] + > = = j j st t ds e s F j s F t f σ π 0 ) ( 2 1 ) ( ) ( 1 L
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Partial Fraction Expansion PFE is method to expand fractions with complicated polynomials for numerator & denominator into sum of fractions Denominators are factors of original denominator Time domain equivalent is in charts PFE breaks down: Into: 0 1 1 1 ) ( ) ( ) ( a s a s a s s N s D s N n n n + + + + = ) ( ) ( ) ( ) ( 2 ω σ j s D c s C b s B a s A s D s N ± + + + + + + + + =
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Roots 3 possibilities for roots: factors of s = roots
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4. Inverse laplace_upload - Inverse Laplace Transform JIN...

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