Laura Jaimes Ramirez 2014360408Ejercicio RCL Ecuaciones Diferenciales

e(t)= L di/dt + iR + i/C qL d2q / dt2 + R dq/dt + 1/C q = e(t)Sustituyendo valores se obtiene la ecuacin diferencial:d2q / dt2 + 160 dq/dt + 10-4q = 20(s2 + 160s +10-4)Q(s) = [sq(0)+q(0)] + 160(0)+ 20/sq(0)= 0q(0) = 0i(0) = 0(s2 + 160s +10-4)Q(s) = 20/sQ(s) = 20/ s (s2 + 160s +10-4)Q(s) = 1/500 / s (1/500) s + 160 / s2+ 160 s +10-4= 1/500 [1/s (s+80)+4/3(60)/ (s+80)2 + (60)2]= 1/500 [[1/s (s)+4/3(60)/ (s)2 + (60)2 ]ss+80]

La solucin general es:I(t)= 1/3 e-80t sen60t