Question

Determine and plot, for the system of Figure P6.40, its response i(t) (a) when v(t) = 10_(t), (b) when v(t) =10u(t), and (c) when v(t)=0.5t.

6.40 Determine and plot, for the system of Figure P6.40, its response i(1) (a) when r(t) 100(1), (b) when y(t) = 10u(t), and (c) when v(t) 0.51. 0.2 H m (1) 2.62 0.1 F FIG. P6.40

Answer 1

6:40) a) Given Vlt)=108(t) .25 Laplace transform Circuit Ils) 2.6 VIS) :: Vis): 10 By mesh equation vis) 2.6toast I15)-1 Ils) (ixios 15 u 10x10 S 2.6x1675 7.2x10+52 +1 50S 32+ 135 +5x10 Ils) 50S (5 +6.5)2 +170712 Now add 6.5 and subtract 6.5 in numeral sols 5 +6.5) -6.5) (5+6.5) + (7071) Ils) Ils) = 7071 325 x 5015+6:5) 15+6.5) +(7071) 7071 (5+6.5)2+(2071 take inverse laplace transform we -6.st will get llt) - 50 é cos(7071) 6.st .046 € sin( 7071t

b). Vt loult) sol VO)- 10 1% Now by circuit I(S) VIS) 2.6 + 25 t 109 Ils) - Sovis) -2 ( 52 + 135 + 5x167] - (1) V659=10 Ils) - 50 Is +6.5)2+(7071) 7071 7071 Ils) (5+65)2 +(707172 take Laplace innerse of ICS ilt) = .007 6.5t sin (7071)+ c). v(t)=.5t V05) - Se Now by circuit &q.(i) Ils) S.VUS) •2 [32 +135 + 5x107] Ils) -2.5 BS+C 2.5 = s $(576.55+ (507132? take partial fraction A f spf576.512417071)? {1s+6.5 52 +35+ 5x109} +352 +cs S 6:5)? + +(30915? } 2.5 -A = Aqs²

ov ASS 5x168 Compare coothicient s, sh and constant At Bro 13 ATC= sxlo7 A = 5X100% BE-5X1 C--13X5X10% (=-65X10-s + $15x108) - 65x108 75+6.5) + (7071)2 Now add and subtract 6.5 in numerator of IOS) - .8 5x10 s second term 8 = sxio -8 t 1:715) = 5x16° 765X160){S+6.5 -6.5} - 65X168 15+6.5)2 4(7071)? - 5x108 (5+6-5) - 32.Sx 7071 (5+6:5)2+(7071)2 707 1 *5+6+381(767 take inness o Ily) Cos (70717 -4.6x10 ē sin(70717) Kaplace 1/" .6.5t est {(t) = 5x10 sxioo ? ilt) = 5x108 [1-6-6.5t [1-665€ (05(7021)} = 9-2X16" sin(1071).
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