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why am i getting grey figure box can someone fix please

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% Constants
g = 9.81; % Acceleration due to gravity
L = 1.0; % Length of the pendulum
t = linspace(0, 20, 1000); % Time vector
% Loop through each initial condition
initial_conditions_list = [0.5; 1.0; 1.5; pi];
for i = 1:length(initial_conditions_list)
figure; % Create a new figure for each initial condition
theta0 = initial_conditions_list(i);
% Analytical solution (from A4)
theta_A4 = theta0 * cos(sqrt(g/L) * t);
% Numerical solution (from A6)
initial_conditions = [theta0; 0];
[t_numerical, Y] = ode45(@(t,Y) pendulumODE(t,Y,g,L), [0 20], initial_conditions);
theta_A6 = Y(:, 1);
% Plotting analytical solution
plot(t, theta_A4, 'r-', 'LineWidth', 2);
hold on;
% Plotting numerical solution
plot(t_numerical, theta_A6, 'b--', 'LineWidth', 2);
hold off;
xlabel('Time (s)');
ylabel('Theta (radians)');
title(['Initial Theta = ', num2str(theta0), ' radians']);
legend('Analytical Solution', 'Numerical Solution');
grid on;
end
Unrecognized function or variable 'pendulumODE'.

Error in solution>@(t,Y)pendulumODE(t,Y,g,L) (line 19)
[t_numerical, Y] = ode45(@(t,Y) pendulumODE(t,Y,g,L), [0 20], initial_conditions);

Error in odearguments (line 92)
f0 = ode(t0,y0,args{:}); % ODE15I sets args{1} to yp0.

Error in ode45 (line 104)
odearguments(odeIsFuncHandle,odeTreatAsMFile, solver_name, ode, tspan, y0, options, varargin);
  2 Comments
Voss
Voss on 4 Jan 2024
Edited: Voss on 4 Jan 2024
Unable to run the code: The function pendulumODE is undefined (see above).
Sulaymon Eshkabilov
Sulaymon Eshkabilov on 4 Jan 2024
As @Voss pinpointed the function file or function handle (anonymous function) called pendulumODE(t,Y,g,L) is missing.
It can be defined as an anonymous function or function file per se.

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Answers (1)

Alan Stevens
Alan Stevens on 5 Jan 2024
Edited: Alan Stevens on 5 Jan 2024
Making some assumptions about your function pendulumODE, I think the following is more like what you expect to see:
% Constants
g = 9.81; % Acceleration due to gravity
L = 1.0; % Length of the pendulum
t = linspace(0, 20, 100); % Time vector
% Loop through each initial condition
initial_conditions_list = [0.5; 1.0; 1.5; pi];
for i = 1:length(initial_conditions_list)
figure; % Create a new figure for each initial condition
theta0 = initial_conditions_list(i);
% Analytical solution (from A4)
w = sqrt(g/L);
theta_A4 = theta0 * cos(w * t);
% Numerical solution (from A6)
initial_conditions = [theta0; 0];
[t_numerical, Y] = ode45(@(t,Y) pendulumODE(t,Y,g,L), [0 20], initial_conditions);
theta_A6 = Y(:,1);
% Plotting analytical solution
plot(t, theta_A4, 'r-', 'LineWidth', 2);
hold on;
% Plotting numerical solution
plot(t_numerical, theta_A6, 'b--', 'LineWidth', 2);
hold off;
xlabel('Time (s)');
ylabel('Theta (radians)');
title(['Initial Theta = ', num2str(theta0), ' radians']);
legend('Analytical Solution', 'Numerical Solution');
grid on;
end
function dthetavdt = pendulumODE(~,Y,g,L)
theta = Y(1); v = Y(2);
w = sqrt(g/L);
dthetavdt = [v; -w^2*theta];
end

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