Determinate the maximum

I have two functions in the same graphic. I need to calculate each maximum. Can somebody help me with the code that I need to put in the EDITOR?

I send a reduce EDITOR:

M=0.577; 
mv=1000; 
A=1.157*10^-5; 
xg0=0.05; 
w0=5.17; 
wf=5.17; 
beta=2/100; 
alfa=0.7; 
L=0.734; 
g=9.81; 
delta=0.5;
%Equation 1
r=@(t,y) [y(3); y(4); -xg0*w0^2*sin(wf*t)-w0^2*y(1)-2*w0*beta*y(3); 0]; 
[Tr,Yr]= ode45(r,[0 50],[0 0 0 0]);
%System of equations
s=@(t,y) [y(3); y(4); (-(M+mv*A*L)*xg0*w0^2*sin(wf*t)-M*w0^2*y(1)-2*M*w0*beta*y(3)-mv*A*alfa*L*((mv*A*alfa*L*((M+mv*A*L)*xg0*w0^2*sin(wf*t)+M*w0^2*y(1)+2*M*w0*beta*y(3))+(M+mv*A*L)*(-mv*A*alfa*L*xg0*w0^2*sin(wf*t)-2*mv*A*g*y(2)-(1/2)*mv*A*delta*abs(y(4))*y(4)))/(mv*A*L*(M+mv*A*L)-(mv*A*L)^2)))/(M+mv*A*L);(mv*A*alfa*L*((M+mv*A*L)*xg0*w0^2*sin(wf*t)+M*w0^2*y(1)+2*M*w0*beta*y(3))+(M+mv*A*L)*(-mv*A*alfa*L*xg0*w0^2*sin(wf*t)-2*mv*A*g*y(2)-(1/2)*mv*A*delta*abs(y(4))*y(4)))/(mv*A*L*(M+mv*A*L)-(mv*A*L)^2)]; 
[Ts,Ys]= ode45(s,[0 50],[0 0 0 0]);
%Graphic 
plot(Ts,Ys(:,1),Tr,Yr(:,1))
% Effectiveness of the system ????

Tank's.

Answer 1

[nick]

Hello Igor,

To find the maximum values of the functions, you can use 'max' function as shown:

M = 0.577; 
mv = 1000; 
A = 1.157*10^-5; 
xg0 = 0.05; 
w0 = 5.17; 
wf = 5.17; 
beta = 2/100; 
alfa = 0.7; 
L = 0.734; 
g = 9.81; 
delta = 0.5;

% Equation 1
r = @(t,y) [y(3); y(4); -xg0*w0^2*sin(wf*t)-w0^2*y(1)-2*w0*beta*y(3); 0]; 
[Tr, Yr] = ode45(r, [0 50], [0 0 0 0]);

% System of equations
s = @(t,y) [
    y(3); 
    y(4); 
    (-(M+mv*A*L)*xg0*w0^2*sin(wf*t)-M*w0^2*y(1)-2*M*w0*beta*y(3)-mv*A*alfa*L*((mv*A*alfa*L*((M+mv*A*L)*xg0*w0^2*sin(wf*t)+M*w0^2*y(1)+2*M*w0*beta*y(3))+(M+mv*A*L)*(-mv*A*alfa*L*xg0*w0^2*sin(wf*t)-2*mv*A*g*y(2)-(1/2)*mv*A*delta*abs(y(4))*y(4)))/(mv*A*L*(M+mv*A*L)-(mv*A*L)^2)))/(M+mv*A*L);
    (mv*A*alfa*L*((M+mv*A*L)*xg0*w0^2*sin(wf*t)+M*w0^2*y(1)+2*M*w0*beta*y(3))+(M+mv*A*L)*(-mv*A*alfa*L*xg0*w0^2*sin(wf*t)-2*mv*A*g*y(2)-(1/2)*mv*A*delta*abs(y(4))*y(4)))/(mv*A*L*(M+mv*A*L)-(mv*A*L)^2)
];
[Ts, Ys] = ode45(s, [0 50], [0 0 0 0]);

% Plot the results
figure;
plot(Ts, Ys(:,1), 'b', Tr, Yr(:,1), 'r');
xlabel('Time');
ylabel('Response');
legend('System of Equations', 'Equation 1');
title('Comparison of Two Systems');
grid on;

●

% Calculate and display the maximum values
[max_Ys, idx_Ys] = max(Ys(:,1));
[max_Yr, idx_Yr] = max(Yr(:,1));

fprintf('Maximum of System of Equations: %.4f at time %.4f\n', max_Ys, Ts(idx_Ys));

Maximum of System of Equations: 0.8537 at time 49.8877

fprintf('Maximum of Equation 1: %.4f at time %.4f\n', max_Yr, Tr(idx_Yr));

Maximum of Equation 1: 1.2369 at time 49.8116

Kindly refer to the documentation by executing the following command in MATLAB Command Window to know more about 'max' function:

doc max