solving a second order linear differential equation

Question

Eliraz Nahum 2018-9-23

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回答： Eliraz Nahum 2018-9-23

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)

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Answer 1

Mischa Kim 2018-9-23

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https://ww2.mathworks.cn/matlabcentral/answers/420337-solving-a-second-order-linear-differential-equation#answer_337961

编辑：Mischa Kim 2018-9-23

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])