Week 3 - Solving second order ODEs
clear all
close all
clc
b = 0.05;
g = 9.81;
l = 1;
m = 0.1;
% initial condition
theta_0 = [0;5];
% time point
t_span = linspace(0,10,500);
% solve ODE
[t, results] = ode45(@(t,theta) ode_func(t, theta, b,g,l,m),t_span, theta_0);
plot(t,result(:,1))
hold on
plot(t,result(:,2))
ylabel('plot')
xlabel('time')
additional program for ode
clear all
close all
clc
function [dtheta_dt] = ode_func(t,theta,b,g,l,m)
theta1 = theta(1)
theta2 = theta(2)
dtheta1_dt = theta2;
dtheta2_dt = -(b/m)*theta2 - (g/1)*sin(theta1);
dtheta_dt = [dtheta1_dt; dtheta2_dt];
end
explantion:-
- all general commands are used in the program
- theta is know as degree value
- b = damping coefficent
- g = gravity
- l = length
- m = mass
- time is calculated as t_span
- additional program is used to calculate ode function on this main program
- additional program formula are derived from the given formula in the question
- derived theta are mention as dtheta
- second ode results showed