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+//Example 9.8
+// Natural Response of a Series LRC Circuit
+// From figure 9.17
+L=0.1;
+R=14;
+C=1/400;
+// Since Excitation is zero by definition of natural response ,we set v_s'=0 in standard 2nd order diffrential equation
+// homogeneneous differential equation will be
+// i_L''+(R/L)*i_L'+(1/(L*C))*i_L=0
+s=%s;
+p=s^2+(R/L)*s+(1/(L*C)); // characteristic equation
+//comparing this equation with standard 2nd order diffrential equation we get
+alpha=R/(2*L);
+omega=sqrt(1/(L*C));
+r=roots(p); // roots of characteristic equation
+// Let us assume values for A's
+A_1= -5;
+A_2= 7;
+t=0:0.001:0.1;
+i_l=A_1*exp(r(2)*t)+A_2*exp(r(1)*t);
+plot(t,i_l) // typical plot of Overdamped Response
+xlabel('t')
+ylabel('i_l(t)')
+title("Overdamped Response of series LRC circuit")
+