Question

1. Consider a continuous system whose input x(t) and output y(t) are related by dy(t) + ay(t) = x(t) dt where a is a constant
2. Consider the system in Problem 1. (a) Show that the system is not linear if y(0) = yo 70. (b) Show that the system is line
3. Consider the system in Problem 1. Find the impulse response h(t) of the system.
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Answer #1

+ igit dy It) (t)=710) D dt a is constant if we take the Laplace toons for m of a boup egin (ů with initial condition y = yoA) sta Eaplautif e-at ult) By using partine fraction Concept A of B (s+a) (s+ b) (S+9) (s+b) Sara for fou put I K__ A b-q -atif we take the caplace Transform of een @ without initial conditions . SYs) to a Y15) = res) X (8) (Sub) K YIS) & stay (sth)YIS) = + 115) sta 410) + e.at -gt o eat u (t) =) othes wire zou (a) if y(o)= yo po from past 1(a). SYIS) - Y10) + 9 YIS) = 81lystem system I= e.at 9,811t) + yo ce engt at and yo erat is called nom lineas tom otherwise the -at ayılt) & treated 92Yz (t( 3 if A B alt) 3 paat 4 9, 7210) and ® erat c CB rat yo 20 Then in abone past put yo=o.in. neph ylt) = erat 91411t). enat 9,reen with zeso ine Now we take the laplay pans from of abouy Egh initial conditions, SYIS) faYIS) = x(s) * 13) & stay tis) Y

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