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

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Nikoloz Nikuradze 2020-9-10

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https://ww2.mathworks.cn/matlabcentral/answers/591604-harmonic-oscilation-when-i-plot-f-towards-time-amplitude-is-increasing-i-don-t-know-why-it-should

回答： Bjorn Gustavsson 2020-9-10

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);

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KSSV 2020-9-10

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

Nikoloz Nikuradze 2020-9-10

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);

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Answer 1

Bjorn Gustavsson 2020-9-10

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/591604-harmonic-oscilation-when-i-plot-f-towards-time-amplitude-is-increasing-i-don-t-know-why-it-should#answer_492613

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