Operate the Laplace Transform on the following text{(i) } f(t)=cos(3t) text{(ii) } f(t)=t^{frac{1}{2}}

chillywilly12a 2021-01-28 Answered
Operate the Laplace Transform on the following
(i)  f(t)=cos(3t)
(ii)  f(t)=t12
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Expert Answer

estenutC
Answered 2021-01-29 Author has 81 answers
Step 1
to find the Laplace transform of  f(t)=cos(3t) proceed as followsL{f(t)}=L{cos(3t)}
using the formula  L{cos(at)}=s2s2+a2
L{cos(3t)}=s2s2+32
=s2s2+9
therefore,  L{cos(3t)}=s2s2+9
Step 2
to find the Laplace transform of  f(t)=t12 proceed as follows
L{f(t)}=L{t12}
using the formulaL{tn12}=(2n1)!π2nsn+12
put n=1 to get  L{f(t)}=L{t12}
L{t112}=(2(1)1)!π21sn+12
=(1)!π2s1+12
=(1)!π2s32
=π2s32
therefore,  L{t12}=π2s32
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