Question

dt - Solve the following equation for y(t) using Fourier Transforms. dy(t) ? +2y(t) = { 'h(t) where h(t) is the Heaviside function: (0,t=0 h(t)= | 1,20 Note: the solution satisfies ly(t) >0 as t →+00.

Answer 1

Page ④ ANS- Given that tourier eanation dy tt) + ayit) - ethet - dt from Given limits are data h(t) = 0 ,to hCt) =1, t20 dE by using fourier Transformer we can solve the equation ® ffer dyct)) +2 ft (yct)) = ft let hie); It converting Time domain to frecuency domain. fourier Series of above canation given as św.pcco) + 2 fico) - sest het) e Sutat , Just modify the eauation . prot.-Jest hit at

Part ③ limits are Substituting in above eauation Gwfcw) + efw) = , tot Q+Sw) fw) = Citit Sw = (ft- C+ سیاح اس The cauation fourier transformer In taken the as soloution ylt). so yet) = (1+5w) (2 +5w)