MATLAB: Solving a second order linear differential equation

MATLABsecond order linear differential equation

hello everybody, I was trying to solve a simple pendulum second order linear differential equation of the form y''=-(g/l)*sin(y) while using the ode45 function. since it's a second order equation I understood that I have to manipulate the problem, so it will fit the ode45.
The mathematical manipulation I did is described in the attached picture.
I can't understand why my code fails…please help
g=9.8;
l=0.5;
t_span=[0 30];
teta0=deg2rad(60);
F=@(t,q) [q(2);-(g/l)*sin(q(2))];
[t,q]=ode45(@(t,q) F(t,q),t_span,teta0)

Best Answer

Almost there:
 g = 9.8;
 l = 0.5;
 t_span  = [0 30];
 teta0   = deg2rad(60);
 tetad0  = 0;
 F       = @(t,q) [q(2);-(g/l)*sin(q(1))];   % check your derivation
 [t,q_t] = ode45(@(t,q) F(t,q),t_span,[teta0; tetad0])
This is a second order DE so you need two initial conditions, one for teta and one for tetad.
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