2nd degree ODE

i want to solve this equation using ode45 with small angle approx theta =sin(theta)

with following initial conditions

and i made this code with m function

function dot = pend_linear(t,var)

dot=[var(1);sin(var(2))*9.81*-1/0.2];

end

and m file to call ode45 and to compare results with analytic solution without any approx.

[t,s]=ode45(@pend_linear,[0;5],[pi/2,0]);

thetan=s(:,1);

thetae=pi/2+49.*(sin(t)-t);%exact solution

plot(t,thetan,'--r',t,thetae,'b')%numerical sol vs exact

and i get these different sol as an answer

which of them is right and what is wrong with false one

Answer 1

[Torsten]

dot=[var(2);-sin(var(1))*9.81/0.2];

Best wishes

Torsten.

[Mo BO]

:(

[Torsten]

Yes, your analytical "solution" is obviously not correct.

Best wishes

Torsten.