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Voltage is inductor V_(L)=L(d^(2)q)/(dt^(2))Voltage in ressitor V_(R)=R(dq)/(dt)Vullage in Copacitor V_(C)=q//cBy kirchoffs 2^("hed ") lawL(d^(2)q)/(dt^(2))+R(dq)/(dt)+(q)/(c)=E(t)Given L=14quad R=5000chmquad C=0.25 xx10^(-6)fquad E(t)=R_(k){:[:.(d^(2)q)/(dt^(2))+5000(dq)/(dt)+(q)/(25 xx10^(-6))=12],[(d^(2)q)/(dt^(2))+5000(dq)/(dt)+4000000 q=12],[{:m^(2)+5000 m+4000000=0" (chavacteristic "q^(4))],[(m_(1)+4000)(m+1000)=0],[:.q_(c)=c_(1)e^(-4000 t)+c_(2)e^(-1000 t)]:}If Q(t)=A quadQ^(')(t)=0quadQ^('')(t)=0Substitutug in onginal eqh we ... See the full answer