function engr80_august_14_2006_2()

% shows how to use Matlab to animation response of one degree of
% freedom system.
% show the effect of changing the damping of the system on the response.
% by Nasser Abbasi, UCI.

clear all; close all;

t_start = 0;
t_end   = 6;  %final time in seconds.
time_span =t_start:0.001:t_end;

k = 40; % spring stiffness. N/m
m = 5;  % mass, kg

cr = 2*sqrt(k*m);  %critical damping

fprintf('critical damping coef. of system is %f\n',cr);

initial_position = 0;
initial_speed    = 0;

x0 = [initial_position  initial_speed];

% Now start the simulation, change damping.

for c = 0: .5 : cr+.1*cr

    [t,x]=ode45(@rhs,time_span,x0);
    plot(t,x(:,1));
    title(sprintf('Critical damping=%4.1f, current damping coeff. =%4.1f',cr,c));
    ylim([-.1 .5]);
    drawnow;
    pause(.1);

end

grid
%**************************************
% solves m x''+ c x' + k x = f(t)
%**************************************
    function xdot=rhs(t,x)

        xdot_1 = x(2);
        xdot_2 = -(c/m)*x(2) - (k/m)*x(1) + force(t)/m;

        xdot = [xdot_1 ; xdot_2 ];
    end
%********************
% The forcing function, edit to change as needed.
%********************
    function f=force(t)

        P = 100;   % force amplitude
        %f=P*sin(omega*t);

        f=10;  %unit step

        %if t<eps     %impulse
        %   f=1
        %else
        %    f=0;
        %end

        %f=P*t;  %ramp input
    end
end