How to solve pendulum ode function?

Hello I have now spent some hours trying to plot my pendulums for different initial conditions.

I want to plot a linear and a none linear pendulum. With regards to angular velocity

My pendulum functions are:

α''+ (-ω^2*sin(α ) = 0

α''+ (-ω^2 *α = 0

where ω is sqrt(g/L). In my case sprt(9.82/0.5)

with my initial conditions

a(0)=10

Da(0)=0

My code might be all wrong for this, I dont know

***************************************

my code right now:

close all;

clear;

global w a b a0

w=sqrt(9.82/0.5);

a = 0;

b = 10;

a0 = 10;

[T,X] = ode45(@invpen,[0,20],[10,10]);

plot(T,X(:,1),'.',T,X(:,2),'-')

function dx = invpen(~,x)

dx = zeros(2,1);

w=sqrt(9.82/0.5);

dx(1) = x''+(w^2*sin(x));

dx(2) = x''+(w^2*x);

end

[Bjorn Gustavsson]

The linearization of is only true for small angles, you feed it 10 radians, which is something like - and not small enough to approximate sin with a straight line...

Answer 1

[Stephan]

https://de.mathworks.com/matlabcentral/answers/437764-ode45-i-get-wrong-results#answer_354579