Question

Solve the initial value problem, x''+8x' +16x = 1 + 8(t-7), x(0) = x'(0) = 0. Click the icon to view the table of Laplace transforms. Write the solution to the initial value problem. Select the correct choice below and fill-in the answer boxes to complete your choice. (Type exact answers. Simplify your answers.) ift< ift< OB. X(t) = O A. X(t) = if <t< if t2 if t OD. X(t) = OC. X(t) = if t = if t = ift> Graph the solution to the initial value problem. OA. OB. Oc. OD 0.375 0.25- AX 0.54 0.375- 0.25- 0.125- 0-1 0 3.5 7 10.51417.5 0.5- 0.375- 0.25- 0.125- 0- 0 35 10.51417.5 AX 0.5 0.375- 0.25- 0.125 0.125- 0- Ó 3.5 7 10.51417.5 TA 03.5 1 10,51417.5

Answer 1

Solutions ta + 8X! + 16 X = 1 + $(1-7) giren co X(o)=x'lo). byezno, take laßlace thens form of both side -75 s} x(s) +85 x(s) + 16 x/5) Ite S 1 x(s) = (t el). (52 +85+16) It ** ) xls) (5+48 S -75 . s(s+432 + X(s)= (S+4J² -TS takre inverse laßlace transform X(t) = ŕ xis) - s(s+4-12 (5+4)2 זן let; X1) ["(II) +(12) let (I) = S (5+4j? B II = - + + Iln S (S+ 432 (5+4) (S+4)? A to ; B = -ja ;c=- 1 4

Hence 1 Il 1 = 2 165 1615+4) +(3+4) Ľ' (1) - . lett 16 16 + Now nót TS е - (543² By loplace inves rese property if = [F11] flt) Hon I' [es flss] = [['{ Flu) } ]oses flt-a) ult-a) { flt-a) tza tko Hence -75 Iz = 1S+4) fore Fl:= & Q = (8+4j2 i' (F133) = f[+) = tett herce T' (t) = 514-7) 447-73 t 27 = {++ನ್ もく子

Hence xlt) = 4A-7) t - 4 11 It-7) 1 e 16 16 4 ; if t77 -47 _ Xl) = ľ 16 tett 16 f tc7 4 Hence option (B) is conreet,