"must return a column vector" ODE45

Hi all, I am trying to solve a free vibration response problem using ode45, and keep getting the same error. My code is as follows:

%%SOLVE SYSTEM OF (TWO) ODES
clear;clc;close all;

%%Set initial conditions
global xst F d Wn  Wd
xst = 4.81548E-05
t = [0 (15*pi*50)]
F = 940
d = 0.05
x = 0.00021
M = 220
rmax = 0.997496867
k = F/(x*((((1-rmax^2)^2)+(4*(d^2)*(rmax^2)))^0.5))
W = 15*pi
Wn = (k/M).^0.5
c = 2*d*Wn
Ft = x*(((k.^2)+(c.^2)*(W^2)).^0.5)
Wd = 450.787

%%Calculate solution for single ODE
[t,x] = ode45(@systemODEfunc,[0 50],[xst, 0]); 

%%Plot results
plot(t,y(:,1),'- red',t,y(:,2), '- blue')

With the ode45 function being:

function y = systemODEfunc(t,x)
global xst F d Wn Wd

y = zeros(50,2)

%Evaluate x(t)
y(t+1,1) = (exp((-d*Wn*t)))*(xst*cos(Wd*t))

%Evaluate dx(t)
y(t+1,2) = (exp(-d*Wn*t))*(((-d*Wn*(xst*cos(Wd*t)))+(Wd*(-xst*sin(Wd*t)))))

end

No matter what I try I seem to always get the following:

Error using odearguments (line 90)
SYSTEMODEFUNC must return a column vector.

Error in ode45 (line 113)
[neq, tspan, ntspan, next, t0, tfinal, tdir, y0, f0, odeArgs, odeFcn, ...

Error in systemODE (line 22)
[t,x] = ode45(@systemODEfunc,[0 50],[xst, 0]);

Answer 1

[James Tursa]

The derivative function needs to return a derivative column vector at a single point in time, not construct an array of such derivative vectors inside the function. E.g., something like this

function y = systemODEfunc(t,x)
global xst F d Wn Wd

%Evaluate x(t)
y(1,1) = (exp((-d*Wn*t)))*(xst*cos(Wd*t))

%Evaluate dx(t)
y(2,1) = (exp(-d*Wn*t))*(((-d*Wn*(xst*cos(Wd*t)))+(Wd*(-xst*sin(Wd*t)))))

end

Side comment: Using global variables to pass in parameters to your derivative function is not good practice. Better to pass them in via a function handle. E.g.,

function y = systemODEfunc(t,x,xst,F,d,Wn,Wd)

%Evaluate x(t)
y(1,1) = (exp((-d*Wn*t)))*(xst*cos(Wd*t))

%Evaluate dx(t)
y(2,1) = (exp(-d*Wn*t))*(((-d*Wn*(xst*cos(Wd*t)))+(Wd*(-xst*sin(Wd*t)))))

end

and then in your calling routine simply use this function handle:

@(t,x) systemODEfunc(t,x,xst,F,d,Wn,Wd)

[Rodolfo Agustin Hernandez]

Thanks very much. This helped me complete my assignment on time.