function Lab2_ODE_solver
% This file applies to question 2
    function dy=myODE(t,y)
    % k - spring constant
    % m - mass
    % In order to solve a 2nd order ODE in Matlab, we need to turn it into
    % a system of 2 1st order ODEs.
    dy1=y(2); %y_1' = y_2
    dy2=-(k/m)*y(1); % y_2' = the right hand side in y_1''
    dy=[dy1;dy2];
    end

% initial conditions y(0)=y0_1 and y'(0)=y0_2
y0=[5; 0];
% time interval
t=0:0.1:4;

% Solving the ODE for different values of the parameters
%%%% Try different values for k and m to answer the questions in your lab
k=1; 
m=1;
[t,y1]=ode45(@myODE, t, y0);

%%%% Try different values for k and m to answer the questions in your lab
k=1; 
m=10;
[t,y2]=ode45(@myODE, t, y0);

% y1(:,1) is the displacement for the first choice of parameters
% y1(:,2) is the velocity for the first choice of parameters

plot(t,y1(:,1),'-o', t,y2(:,1),'-*')
legend('displacement, k=1,m=1', 'displacement, k=1,m=10')
end