function VTB1_1(m,c,k,x0,v0,tf)%VTB1_1 Free response of a single degree of freedom system.% VTB1_1(m,c,k,x0,v0,tf) plots the free response of a single degree % of freedom system.  The arguments x0 and v0 represent the initial % conditions and tf represents the total time of the response. The% system is described by mass m, damping c, and stiffness k.% VTB1_1(zeta,w,x0,v0,tf) plots the free response of a single degree % of freedom system.  The arguments x0 and v0 represent the initial % conditions and tf represents the total time of the response.% The system is in non-dimensional form, where zeta is the damping% ratio, and w is the natural frequency in rad/s.%clc% This loop determines which type of input format you are using.if nargin==5  z=m;w=c;tf=v0;v0=x0;x0=k;m=1;c=2*z*w;k=w^2;endw=sqrt(k/m);z=c/2/w/m;%(1.30)wd=w*sqrt(1-z^2);%(1.37)fprintf('The natural frequency is %.3g rad/s.\n',w);fprintf('The damping ratio is %.3g.\n',z);fprintf('The damped natural frequency is %.3g.\n',wd);t=0:tf/1000:tf;if z < 1    A=sqrt(((v0+z*w*x0)^2+(x0*wd)^2)/wd^2);%(1.38)    phi=atan2(x0*wd,v0+z*w*x0);%(1.38)    x=A*exp(-z*w*t).*sin(wd*t+phi);%(1.36)    fprintf('A= %.3g\n',A);    fprintf('phi= %.3g\n',phi);  elseif z==1    a1=x0;%(1.46)    a2=v0+w*x0;%(1.46)    fprintf('a1= %.3g\n',a1);    fprintf('a2= %.3g\n',a2);    x=(a1+a2*t).*exp(-w*t);%(1.45)  else    a1=(-v0+(-z+sqrt(z^2-1))*w*x0)/2/w/sqrt(z^2-1);%(1.42)    a2=(v0+(z+sqrt(z^2-1))*w*x0)/2/w/sqrt(z^2-1);%(1.43)    fprintf('a1= %.3g\n',a1);    fprintf('a2= %.3g\n',a2);    x=exp(-z*w*t).*(a1*exp(-w*sqrt(z^2-1)*t)+a2*exp(w*sqrt(z^2-1)*t));%(1.41)endplot(t,x)xlabel('Time')ylabel('Displacement')title('Displacement versus Time')text(0,0,'Press Return To Continue','sc')