Find the inverse laplace transform of frac{6s+9}{s^2+17} s>0 y(t)=dots

Amari Flowers 2020-10-26 Answered
Find the inverse laplace transform of
6s+9s2+17s>0
y(t)=
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Expert Answer

i1ziZ
Answered 2020-10-27 Author has 92 answers
Step 1
Given the Laplace transform of a function y(t) such that
L{y(t)}=6s+9s2+17
Find f(t) using inverse Laplace transform.
Step 2
First, separate the numerator.
6s+9(s2+17)=6s(s2+17)+91(s2+17)
Since L1{a(s2+a2)}=sin(at) , multiply the numerator and denominator on the second sum by 17
6s+9(s2+17)=6s(s2+(17)2+9(17)17s2+(17)2
Step 3
Now, take inverse Laplace transform on both sides.
L1{6s+9(s2+17)}=6L1{ss2+(17)2}+917L1{17s2+(17)2}
Since L1{a(s2+a2)}=sin(at) and L1{s/(s2+a2)}=cos(at)
L1{6s+9(s2+17)}=6cos(17t)+9/(17)sin(17t)
Therefore, y(t)=6cos(17t)+9(17)sin(17t)
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