Question: a. Writing the loop equation, Ri+Ldidt+1Cidt+vC(0)=v(t)b. Differentiating and substituting values, d2idt2+2didt+30i=0Writing the characteristic equation and factoring,M2+2M+30=(M+1+292i)(M+1-292i)The general form of the solution and its derivative isi=e-tcos(292t)A+(Bsin(292t))e-tdidt=(-A+292B)e-tcos(292)-(292A+B)e-tsin(292t)Usingi(0)=0;didt(0)=vL(0)L=1L=2i(0)=A=0didt(0)=-A+292B=2Thus,

a. Writing the loop equation, Ri+Ldidt+1Cidt+vC(0)=v(t)b. Differentiating and substituting values, d2idt2+2didt+30i=0Writing the characteristic equation and factoring,M2+2M+30=(M+1+292i)(M+1-292i)The general form of the solution and its derivative isi=e-tcos(292t)A+(Bsin(292t))e-tdidt=(-A+292B)e-tcos(292)-(292A+B)e-tsin(292t)Usingi(0)=0;didt(0)=vL(0)L=1L=2i(0)=A=0didt(0)=-A+292B=2Thus, A=0 and B=2292.The solution isi dont know why v_L(0) is 1, at solution di/dt(0) is 2 so i'm confused..

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