Harmonic Oscilation. When I plot f towards time amplitude is increasing I don't know why. It should be constant. what's wrong?

When I plot f towards time amplitude is increasing I don't know why. It should be constant. what's wrong?

for i= 1:N
    t(i+1)=t(i)+dt;
    
    E(i)=-f(i); % Equation for the z axial motion
    
    w(i+1)=w(i)+E(i)*dt;
  
    f(i+1)=f(i)+w(i)*dt;
   
    
end
plot(t,f);

[KSSV]

No variable value is given here....how do you expect us to help you?

[Nikoloz Nikuradze]

f(1)=3;    %% Ratation angle (Rad)
w(1)=0;    %% Angular velocity (Rad/sec)
E(1)=0;    %% Angular acceleration

t(1)=0;    %% Time vector (sec)
dt=0.001;

N=1000000;
%% The main code
for i= 1:N
    t(i+1)=t(i)+dt;
    
    E(i)=-f(i); % Equation for the z axial motion
    
    w(i+1)=w(i)+E(i)*dt;
  
    f(i+1)=f(i)+w(i)*dt;
   
    
end
plot(t,f);

Answer 1

[Bjorn Gustavsson]

Well if you have an equation of motion you should write it as an ordinary differential equation and solve it with a more ambitious method than the "explicit-Euler"-looking method you've chosen. Have a look at ode45 and its siblings. It seems pretty likely that at least one example of ODE-integration in the help, documentation and demos for the ode45, ode23 etc functions explicitly deals with harmonic oscillations. You likely can find some analysis of the expected long-term behaviour of explicit Euler-methods for this case if you search the internet.

HTH