Find the inverse Laplace transform f(t) of the following transforms F(s). Match each of the...

Danelle Albright

Danelle Albright

Answered

2021-12-28

Find the inverse Laplace transform f(t) of the following transforms F(s). Match each of the following to the value of f(1.234) to two decimal places.

Answer & Explanation

nghodlokl

nghodlokl

Expert

2021-12-29Added 33 answers

Inverse Laplace Lt{9s+13s2+2s+10}
Lt{9s+9+4s2+2s+10}
=Lt{a(s+1)+4(s+1)2+9}
=9Lt{s+1(s+1)2+9}+4Lt{1(s+1)2+9}
=9etLt{ss2+9}+4etLt{1s2+9}
Using Lt{F(sa)}=eatt(t) (formula)
=9etcos3t+43sin3t
Hence Lt{9s+13s2+25+10}=9etcos3t+43etsin3t=f(t) (1)
Now f(1.234) (2)
From (1) and (2)
f(1.234)=9e(1.234)cos(3(1.234))+43e(1.234)sin(3(1.234))
=2.42
Mason Hall

Mason Hall

Expert

2021-12-30Added 36 answers

a) F(s)=9s+352+28+10
L1{9s+3s2+28+10}=2
9s+3s2+28+10=9(s+1)(s+1)2+9=61(s+1)2+9
L1{9s+3s2+28+10}=L1{9(s+1)(s+1)2+96(s+1)2+9}
=9L1{s+1(s+1)2+9}6L1{1(s+1)2+9}
=9etcos(3t)6et×13sin3t
=9etcos(3t)2etsin3t
F(s)=5228+154453+105212+5
Take partial fraction of
5228+454453+1052125+5=34(51)2+14(5228+5)
L1{5225+454453+1052125+5}=Lt{34(51)2+14(5228+
karton

karton

Expert

2022-01-10Added 439 answers

Lt{9s+13s2+2s+10}Lt{9s+9+4s2+2s+10}=Lt{a(s+1)+4(s+1)2+9}=9Lt{s+1(s+1)2+9}+4Lt{1(s+1)2+9}=9etLt{ss2+9}+4etLt{1s2+9}Lt{F(sa)}=eatt(t) (formula)=9etcos3t+43sin3tLt{9s+13s2+25+10}=9etcos3t+43etsin3t=f(t) (1)f(1.234) (2)f(1.234)=9e(1.234)cos(3(1.234))+43e(1.234)sin(3(1.234))=2.42

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