Trying to solve and plot the non-linear pendulum equation

Hi! I have the d^2/dt^2 + g/L(sinθ)=0 2nd order D.E. (Simple Pendulum) which I have seperated to two 1st order D.E.

y(1) = dθ/dt = ω = u_θ , y(2) = dω/dt = -b^2*sinθ (where b = sqrt(g/L))

I want to use ode45 to solve these equations.

I tried following the link: https://www.mathworks.com/help/matlab/ref/ode45.html but I got errors on my code.

m-file

function dydt = spendn(t,y)
dydt = [u; -sinu];

In command window:

[t,y] = ode45(@spendn,[0 7],[0; 1.57]);

I am doing something wrong here, pls help.

[Jan]

Please post the complete error message.

The conversion from

y(1) = dθ/dt = ω = u_θ
y(2) = dω/dt = -b^2*sinθ (where b = sqrt(g/L))

to

dydt = [u; -sinu];

seems to be too rough. Neither "u" not "sinu" are defined.

Answer 1

[Star Strider]

Try this:

dydt = [u; -sin(u)];

[Star Strider]

Alexandros’s “Answer” moved here:

This is the error:

Undefined function or variable 'u'.

Error in spendn (line 9)
dydt = [u; -sin(u)];

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

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

[Star Strider]

The complete correction is:

function dudt = spendn(t,u)
dydt = [u; -sin(u)];
end

[Alexandros]

Now I get this error:

Error using odearguments (line 92)
SPENDN returns a vector of length 4, 
but the length of initial conditions vector is 2. The
vector returned by SPENDN and the initial conditions 
vector must have the same number of
elements.

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

[Star Strider]

Use this:

function dudt = spendn(t,u)
dydt = [u(2); -sin(u(1))];
end

or this:

spendn = @(t,u) [u(2); -sin(u(1))];

Either of these will work.