function Lab2_ODE_solver_near_res
% This file applies to:
% Question 5 - be careful to set b=0
% Question 8 - be careful to set b as requested in the lab
    function dy=myODE(t,y)
    % k - spring constant
    % m - mass
    % Frequency om=sqrt(k/m)
    dy1=y(2);
    dy2=-om^2*y(1)-b*y(2)+cos(om0*t);
    dy=[dy1;dy2];
    end

% initial conditions
y0=[5; 0];
% time interval
t=0:1:100;
%natural frequency
om=1;
%forcing frequency
om0=1.005;
%damping
b=0;
[t,y1]=ode45(@myODE, t, y0);

%%%%%% Trying with different parameters
%natural frequency
om=1;
%forcing frequency
om0=1.5;
%damping
b=0;
[t,y2]=ode45(@myODE, t, y0);

%%%% A plot comparing the two solutions
plot(t,y1(:,1),'-', t,y2(:,1),'--')
legend('displacement, om=1, om0=1.005',  'displacement, om=1, om0=1.5')
end