Question

FOUR-Matlab Solve the following equation of motion using Matlab ODE45: 4 -m 6(0) 6(0)-0.1 (0) 0.2 0(0)-1 Assume that: m-0.1 kg, g-10 m/s, L-1 m, r-0.5 m. Plot θ vs 1 and θ vs θ

solve with matlab

Answer 1

s (2) ma Lcose-mr 2

Hence, our deivative vecor ubiil be S(4) 4 The ode function

Here is the odefunction :

and Script for solving:

9 8 7 6 5 θθ 4 3 2 0 432 0-1-2-3-4-5 |

Text:

Function :

function dsdt = odefunction(t,s)
m = 0.1;
g = 10;
L = 1;
r = 0.5;
dsdt = zeros(2,1);      % initializing dsdt

dsdt(1) = s(2);         % Setting 1st element
dsdt(2) = (-3/4)*(m*g*L*cos(s(1)) + m*r^2)/(m*L^2);     % 2nd element

Script :

s0 = [pi/6 0.1];        %Initial Conditions [theta(0) theta_dot(0)]
tspan = [0 10];         % time span
[t,s] = ode45(@(t,s) odefunction(t,s),tspan,s0);     % Solving ODE

% t is time vector and s is solution vector
plot(t,s(:,1))            % plot theta vs t
hold on
plot(t,s(:,2))            % plot theta_dot vs t
legend(["\theta","\theta dot"],'Location','Best')
xlabel("Time [sec]")
% recall our assumptions s(1) = theta, s(2) = theta_dot