Solue using partial fractions F(S)=\frac{-4s}{(s^{2}+4)^{2}}

illusiia

illusiia

Answered question

2021-09-28

Solue using partial fractions
F(S)=−4s(s2+4)2

Answer & Explanation

ensojadasH

ensojadasH

Skilled2021-09-29Added 100 answers

Step 1
F(s)=−4s(s2+4)2
Partial form:
−4s(s2+4)2=As+B(s2+4)2
−4s=As+B
A=−4, B=0
Laplace Properties:
L−1[f(s)]=F(t)
L−1[f(s)]=ddtF(t)+F(g)
L−1[−4s(s2+4)2]=−L−1[s{4(s2+4)2}]
=−L−1[s]=−[ddt{F(t)}+F(g)]
=−ddtL−1[4(s2+4)2]+L−1[4(s2+4)2]{0}
Step 2
=L−1[4(s2+4)2]=14[sin⁡2t−2tcos2t]{0}
ddt[L−1(4(s2+4)2)]=14ddt[sin⁡2t−2tcos⁡2t]
ddt

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