Solve f(t)=e^t cos t

UkusakazaL 2020-11-01 Answered
Solve f(t)=etcost
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Expert Answer

averes8
Answered 2020-11-02 Author has 92 answers
Step 1
We have to form Laplace transform integral first.
Step 2
We have f(t)=etcost
We know that,
F(s)=0estf(t)dt
F(s)=0cos(t)e(1s)tdt
by integrath by pcuts
F(s)=[cos(t)e(1s)t1s]0+(e(1s)t1s)sintdt
F(s)=11s+11s[e(1s)tsint1s]0(e(1s)t1s)costdt
F(s)=11s1(1s)2
F(s)[1+1(1s)2]=1(1s)
F(s)=(1s)2(1s)[(1s)2+1]
F(s)=s1[(s1)2+1]
Answer: F(s)=s1[(s1)2+1]
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