Question

Create a Matlab code using ode45 function to solve the following two equations of a pendulum:

m+M)x'' - ml$\Theta$'' cos$\Theta$ + ml$\Theta$'' sin$\Theta$ = F

-x'' cos$\Theta$ + l$\Theta$'' - g sin$\Theta$ = 0

Force = 10N

5kg pendulum

initial angle = 30

Answer 1

COS

T CoS

solve for

T, , and0"

COS

$-x''+(l/cos\theta)\theta'' = gtan\theta$

$-(M+m)x''+(M+m)(l/cos\theta)\theta'' = (M+m)gtan\theta$

add the two equations

ーCOS

mqtan M +m)(/cost

le) cost

Matlab Code:

clear;clc;
syms t;
init = [1,pi/6,0,0];% initial conditions
[t,y] = ode45(@f,[0 10],init);

plot(t,y(:,1));
hold on;
plot(t,y(:,2));

function dydx = f(t,y)
M = 10;m = 5;F = 10;l = 1;g = 9.8;
dydx = zeros(4,1);
dydx(1) = y(1);
dydx(2) = y(2);
dydx(3) = ((M+m)*g*tan(t)+F)/((M+m)*(l/cos(t))+m*l*(sin(t)-cos(t)));
dydx(4) = (l*dydx(3) - g*sin(t))/(cos(t));
end