Question

Find the Laplace transform of the function f(t). f(t) = sin 3t if 0 <t< < 41; f(t) = 0 ift> 41 5) Click the icon to view a short table of Laplace transforms. F(s) = 0

Answer 1

f(t) = sin 3t f(t) = 0 if oct & 4T if t> 41 s sín 3t Osts 4T Ict) = s sin 1 0 t? UTT write af Heaviside step function : $te) = sin at [uce-o) – U(E-40)] + 0 [bet-u0)] $1t) = sinut ult) - sin 3t Uſt-45) | +(t) = sin ut ult) - SEN 3 (t-4T) .ut-41) we know that Z{ F(t-a) u (t-a)} = eas f(s). :: X{ sinst } - present et sihat? - ed *{ uinut vos fa Zą sio 3 -ut) vlt=40)} = d .create ::t{$s} seam en -405 U+.32 -UUS FCD) - [-ény

from Basic Law n3t / af staat} = jotta su Barte don e f(t) dt a sinst dt + lo est at 40 1 4TT. F (s) = lést sín 3t dt It fogod porn som det po! I• Section departe I = -st 3 cos3t = [stat entre els cast 3* do 7 - Sinat ēst cos3t 31 - I: sin 37 ést - Cos3t ē e -3 с 2. = (19) - [ HXH. 2. are at a IH sinut ast -40s I YUS