Wiley signals and systems e book TLFe BO 165

a) the hornogenous solution ytl ( f ) 1)) a par ticitlar solution g,(t) (a) tlir c*nmpletesolution y ( f ) IndicatP tlic intprnnl arid c>xlcrnal part s of the ~1iitio1-i E x e r ~ ~ '9.3 se Soli e the init i d cwnditioii p ~ o b l e ~ ~ i > c1 r ( t )- 10 cos(&), c > fj(f) i- 3y(t) = x ( t ) , f d(l+) = &I transform Considci tlw initial conclititxis usiiig IJie rliffei.pn{iittion tlieorem IOL tlw nriilitteral I ~ p I a c ctransform (4.34) its ~ h o w nin Sectioxi 7.1.2 Del eririirie a) N(s) h) Y j s ) c) y(l) for f ;0 Exercise 7.4 Derive equation (7.16) froiii (7.15) itsiiig tlw differtiitiation theorem of the Laplace tri ansform (4.34) Exercise 7,5 Thr followiiig fii st-ordcr hystcm i s givm a's a block diagram: z(t) = E(t) 40) - 20 ' (1 - t) + E(f 1) (t - 1) Ueteriniiic a) the Ini(ia1values y(O-) aiid #(U+)