How to graph an ODE45

I have two scripts one with a split second order differential equation into two one order differential equation and the other is meant to call it and solve a ode45 with that and show a graph but it doesnt seem to work im getting an error with the first order differential equation. Please tell me where i have gone wrong and how to fix it.

 function dX=MSD_numerical_equation(t,X,m,b,k)
%
% We need to split the 2nd order differential equations for the 
% mass-spring-damper in to 2 1st order differential equations so they are 
% of a suitable form for Matlab to solve (e.g. with ODE45)
%
% we obtain the derivative for each of the variables
% (position and velocity of the particle)
%
t=0;
X=0;
% The first column : the particle position
% The second column : the particle velocity
% m,b,k: parameters for the system
m=10;
b=5;
k=160;
% Apply two 1st order differential equations
%dx(n+1)/dt<-v(n);
dX(1,1)=X(2,1);
%dv(n+1)/dt<-1/m*(F0sin(wt)-bv(n)-kx(n));
dX(2,1)=(1/m)*(-b*X(2,1)-k*X(1,1));
end
%
%Second script
%
%
function O=MSD_ode45(m,b,k,x0,v0,dt)
%
% Solver for Mass-Spring-Damper System with high order Runge-Kutta Method
%
% NO FORCING TERM INCLUDED
%
% ----- Input argument -----
m=10;
b=5;
k=160;
x0=1;
v0=0;
dt=0.02;
%
options=odeset('InitialStep',dt,'MaxStep',dt);
% set time span to be generated from Runge-Kutta solver
% from 0 sec to 20 sec with 0.02 sec time step
td=[0:dt:20];
% Solve differential equation with Runge-Kutta solver
[t,x]=ode45(@(t,X)MSD_numerical_equation(t,X,m,b,k),td,[x0;v0],options);
% Extract only particle position trajectory
O=[t x(:,1)];
plot(t,x(:,1))
hold on
xlabel('time (s)')
ylabel ('height (m)')
end

[Star Strider]

What error is it throwing?

Please copy the entire error message — all the red text in your Command Window — and post it here.

[omar El Olimi]

First script: >> MSD_numerical_equation Index exceeds matrix dimensions.

Error in MSD_numerical_equation (line 21) dX(1,1)=X(2,1);

Second script: >> MSD_ode45 Index exceeds matrix dimensions.

Error in MSD_numerical_equation (line 21) dX(1,1)=X(2,1);

Error in MSD_ode45>@(t,X)MSD_numerical_equation(t,X,m,b,k) (line 20) [t,x]=ode45(@(t,X)MSD_numerical_equation(t,X,m,b,k),td,[x0;v0],options);

Error in odearguments (line 87) f0 = feval(ode,t0,y0,args{:}); % ODE15I sets args{1} to yp0.

Error in ode45 (line 115) odearguments(FcnHandlesUsed, solver_name, ode, tspan, y0, options, varargin);

Error in MSD_ode45 (line 20) [t,x]=ode45(@(t,X)MSD_numerical_equation(t,X,m,b,k),td,[x0;v0],options);

Thank you for helping:)

[omar El Olimi]

It may also be because of the t and X because i didnt understand what they were for so i just made them as 0. It was stated before that they were:

1. t: current time.
2. X: matrix for state variables.
3. The first column : the particle position.
4. The second column : the particle velocity.
5. m,b,k: parameters for the system.

[Tamir Suliman]

I think this is all confusing what you trying to do you will have to format the question in a way that explains it well and explains what u trying to

please post the equation you modelling I realized tha you passing values through the function input variables like t X while you already have their values assisnged on the script any idea why u doing this ? your first function :

 function dX=MSD_numerical_equation(t,X,m,b,k)
%
% We need to split the 2nd order differential equations for the 
% mass-spring-damper in to 2 1st order differential equations so they are 
% of a suitable form for Matlab to solve (e.g. with ODE45)
%
% we obtain the derivative for each of the variables
% (position and velocity of the particle)
%
t=0;
X=0;
% The first column : the particle position
% The second column : the particle velocity
% m,b,k: parameters for the system
m=10;
b=5;
k=160;
% Apply two 1st order differential equations
%dx(n+1)/dt<-v(n);
dX(1,1)=X(2,1);
%dv(n+1)/dt<-1/m*(F0sin(wt)-bv(n)-kx(n));
dX(2,1)=(1/m)*(-b*X(2,1)-k*X(1,1));
end
%

Your second Function

function O=MSD_ode45(m,b,k,x0,v0,dt)
%
% Solver for Mass-Spring-Damper System with high order Runge-Kutta Method
%
% NO FORCING TERM INCLUDED
%
% ----- Input argument -----
m=10;
b=5;
k=160;
x0=1;
v0=0;
dt=0.02;
%
options=odeset('InitialStep',dt,'MaxStep',dt);
% set time span to be generated from Runge-Kutta solver
% from 0 sec to 20 sec with 0.02 sec time step
td=[0:dt:20];
% Solve differential equation with Runge-Kutta solver
[t,x]=ode45(@(t,X)MSD_numerical_equation(t,X,m,b,k),td,[x0;v0],options);
% Extract only particle position trajectory
O=[t x(:,1)];
plot(t,x(:,1))
hold on
xlabel('time (s)')
ylabel ('height (m)')
end

What I m trying to under stand why do you have to go through multiple functions which adds more complexity instead of using one functions then pass those variables to

[omar El Olimi]

Thank you Tamir for replying, I think this is used because the function in the symbolic script is used in other scripts as well later on, which will make it easier later on. I am having errors on both functions though, do you know why this is coming up?

[Tamir Suliman]

you have X=0

then you have X(2,1) do you think this a right ? what / where is x(2,1)

you will need to fix the matrix if you have other values