Sumudu Transform - Practical Importance

Practical Importance

In mechanical and material engineering, the Laplace–Carson transform

$C\{f(t)\} = G(p) = \int_0^\infty pe^{-pt}f(t)\,dt\qquad(3)$

is used in the study of the behavior of linear visco-elastic materials. When the linear visco-elastic constitutive law is transformed to the Laplace–Carson domain, its integral form reduces to the simple . This is not the case when using the Laplace transform itself. Some other constitutive laws are more appropriately described by the Carson transform,

$Car\{f(t)\} = G_{Car}(p) = p\int_0^\infty e^{-pt}f(t)\,dt\qquad(4)$

with the p in front of the integral.

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