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228_w06_q4b_sol - EE 228 Continuous-Time Signals and...

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Unformatted text preview: EE 228 Continuous-Time Signals and Systems SOIUtiOH Cal Poly, slo Quiz 4 John Saghri A linear time—invariant system with zero-initial conditions is described by the folldwing differential equation. y"(t) + 4 y’(t) + 3 y(t) = X(t) Assume X(t) = u(t) Part a: (2 pints) Obtain yF(t), i.e., the forced component of the total response y(t) Shade )(Qt): HG.) OSSUIMQ YFQC) :3 Met) qufl ’sobgtl'lule eat/l in étfx‘aywl‘lqfl equaln’mn 0+Mo) +BBULU2UUC) ‘3' 3:3; o l n " VF CE -.: E. Lick) Answer: yF(t)= '3— UR.) Part b: (4 pints) Obtain the total response y(t) = yF(t), + yN(t), where yN(t) is the natural response. max/swine— a we me we U56: l'm‘Jn‘ajZ'Conoll'Jn'M JUNE/d («@0ng K52 lea Y(0):Q ——$ L+ki+kg :o y(JCJ=[\§~—‘Z—_ e +‘Z‘e 4?qu 1‘ 1 _J( \ fist Answer: y(t)=i§fl-Ee +g€ ELK-U Part c: (3 pints) Obtain the impulse response h(t) ...
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