Find laplace transform of each following a) displaystyle{t}^{n} b) displaystyle cos{omega}{t} c) displaystyle sin{{h}}{left({c}{t}right)} d) displaystyle cos{{h}}{left({c}{t}right)}

banganX 2020-10-28 Answered
Find laplace transform of each following
a) tn
b) cosωt
c) sinh(ct)
d) cosh(ct)
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Expert Answer

Arham Warner
Answered 2020-10-29 Author has 102 answers
ANSWER FOR (A)We have to find Laplace transform of tn, that is, L{tn}.
Now from the Laplace Transform table we know that
L{tn}=n!sn+1
This shows that
L{tn}=n!sn+1
ANSWER FOR (B) We have to find Laplace transform of cos(ωt), that is, L {cos(ωt)}
Now from the Laplace Transform table we know that
L{cos(at)}=ss2+a2
Whis shows that
L{cos(ωt)}=ss2+ω2
ANSWER FOR (C) We have to find Laplace transform of sinh(ct), that is, L {sinh(ct)}
Now from the Laplace Transform table we know that
L{sinh(at)}=as2a2
Whis shows that
L{sinh(ct)}=cs2c2
ANSWER FOR (D) We have to find Laplace transform of cosh(ct), that is, L {cosh(ct)}
Now from the Laplace Transform table we know that L{cosh(at)}=ss2a2
Whis shows that
L{cosh(ct)}=ss2c2
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