Question

Identify the Laplace transform of the function h(t) = 7 cos (2t - 1) (1). 3.782s 8² + 4 + 11.781 S2 + 4 7s S2 + 4 3.782 8 + 4 O 11.781s + 3.782 S2 + 4 S2 + 4 O 3.782 11.781 S2 + 4 S2 + 4

Answer 1

if it), a Ulit -a) gostea Ques: Identify the haplace Transform of the hap Tare Transform of h(t) = 7 Cos (2 d. Julty function h(t) = of Cos(at 1) ult) Ans:- The Given function h(t) = 7 Cos (at uult) — 0 Now we define The Heaviside unit function Ult-a) for a> o { and use the Result het aso and L {f(tl) = F(S) Then L {flit-a) Ult-a) y = e FLS) Comparing O with 6, we get U(H) = po uj it, o Now hld) = 7 Cos (2d-1) ult) Here azo and flat) = 7 Cos (2 tt) Now flt-a)= ft-o) = 7 Cos Qt-| -as Y* a-o y ocet Now

- 32+4 52 +4 h{ 1 Cos (84)} = FIS) Now F(S) L{ 1 [Cos dt Col + Sinat. Sin 1] sin 1) [: Cos (A-B) = Cos A Los B + sinAsing & F(S) L { 7 Cos 2 et Coss} +L{1 Sin aut sin i} 7 Cost Le Cos2et} + 7 Sin 1 he sinait? 7 Cost x S + 7 Sin 1 2 3244 7 Coslis 14 sini 5244 7X0.5403 xs 5274 [Sin! = 0-841470984 3.70215 Cost = 0.54030 2 2 305] 11.70058 5244 82+4 F(S) = 3702 5 11.781 2244 L{ 7 Cold et +) 4 = 318 25 11:781 by Equation ③ h{f(it -a) Ult-a)} = e FC) 1480.84 147 + satu + S2+4 ME(S) + stu sly to Now

Here azo -O.S e L { Cos (get-1) U (t)} = FLS) 1. ( 2 3.7025 + S2+4 11.781 stu 11.781 $+4 h { Cos (2d+) UL)} = 3.7825 + 82 +4 11:781 + Result :- loption (a) L{hl Hf = 3825 244 Lş Cos (441) Olt)} = 3.782 s 5244 5244 ie + 11.781 8274 (2) a Note - ④ Cos (A-B) = Cos A Cos Bt sina sin B hs sinat} So stad ♡ { Cosat į 52+Q2 S Thanking you