Program Description: Purpose of problem is to obtain the inverse Laplace transformation of given function F ( s ) = 10 s − 3 25 − s 2 . Summary introduction: Program will use the inverse of Laplace transform as given below. cosh k t = L − 1 { s s 2 − k 2 } sinh k t = L − 1 { k s 2 − k 2 } Here, the value of s > | k | . The linearity theorem of the Laplace transform for all s such that the functions f and g both exists is defined as, L { a f ( t ) + b g ( t ) } = a L { f ( t ) } + b L { g ( t ) }

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Chapter 7.1, Problem 31P

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Program Description: Purpose of problem is to obtain the inverse Laplace transformation of given function F(s)=10s−325−s2 .

Summary introduction:Program will use the inverse of Laplace transform as given below.

coshkt=L−1{s s 2− k 2}sinhkt=L−1{k s 2− k 2}

Here, the value of s>|k| .

The linearity theorem of the Laplace transform for all s such that the functions f and g both exists is defined as,

L{af(t)+bg(t)}=aL{f(t)}+bL{g(t)}

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