Plotting harmonic oscillators for different values of Beta

I need to plot harmonic oscillators depending on their beta values. I'm having trouble plotting the data that's in the if/elseif statements. My code is down below.

w0= 4*pi;

x0= 100;

beta= [0, 2, 5, 10, 20,50];

time=linspace(0, 120, 6);

%%Undamped Oscillator

if beta==0

C = 50;

pos_t = C*exp((w0*time)*1i) + C*exp(-(w0*time)*1i);

const = C*w0*1i;

vel_t = const*exp((w0*time)*1i) - const*exp(-(w0*time)*1i);

%%Under-damped

elseif beta< w0

delta = arctan(beta/w0);

A = x0/cos(delta);

pos_t = A*exp(-beta*time)*cos(w0*time - delta);

vel_t = -A*exp(-beta*time)*(beta*cos(w0*time- delta) + w0*cos(omega_0*time));

%%Over-damped

elseif (beta> w0)

gamma_minus = beta - sqrt(beta*beta - w0*w0);

gamma_plus = beta + sqrt(beta*beta - w0*w0);

C2 = x0/(1-(gamma_minus/gamma_plus));

C1 = X0 - C2;

pos_t = C1*exp(-gamma_minus*time) + C2*exp(-gamma_plus*time);

vel_t = -gamma_minus*C1*exp(-gamma_minus*time) - gamma_plus*C2*exp(-gamma_plus*time)

else

pos_t = 0;

vel_t = 0;

end

plot(time, pos_t)

[Chris]

First, try setting beta to a single value.

Otherwise, you would need to for loop through each value and test them individually (you can do this once the plots are all working).

Once beta is no longer a vector, run the script and read the error messages.

For starters, arctan() isn't a standard matlab function. You probably want atan().

Then, you'll need to do some element-wise operations. Replace * and / and ^ with .* and ./ and .^

Otherwise, Matlab thinks you want to do linear algebra, when all you want is to apply an operation to each element of a vector/array.

Good luck! If you have a specific error you can't get past, let us know.

Answer 1

[Mathieu NOE]

hello

as mentionned by @Chris there was some missing dots in element wise operations . Others minor bugs included wrong time vector definition (swap end value and number of points) and other minor things - see comments in the code below

then added the for loop with legend showing how your results look like vs beta

hope it helps !

w0= 4*pi;
x0= 100;
beta_list= [0, 2, 5, 10, 20,50]; % list of beta values


% time=linspace(0, 120, 6);
time=linspace(0, 3, 100);  %   LINSPACE(X1, X2, N) generates N points between X1 and X2.

% plot figure
figure(1),
hold on

for ci =1:numel(beta_list)
    
    beta = beta_list(ci);
    
    %%Undamped Oscillator 
    if beta==0
         C = 50;
         pos_t = C*exp((w0*time)*1i) + C*exp(-(w0*time)*1i);
         const = C*w0*1i;
         vel_t = const*exp((w0*time)*1i) - const*exp(-(w0*time)*1i);

    %%Under-damped 
    elseif beta<= w0   % replaced < with <=
            delta = atan(beta/w0);
            A = x0/cos(delta);
            pos_t = A*exp(-beta*time).*cos(w0*time - delta);
    %         vel_t = -A*exp(-beta*time).*(beta*cos(w0*time- delta) + w0*cos(omega_0*time));
            vel_t = -A*exp(-beta*time).*(beta*cos(w0*time- delta) + w0*cos(w0*time)); % replaced omega_0 with w0

     %%Over-damped 
     elseif (beta> w0)
            gamma_minus = beta - sqrt(beta*beta - w0*w0); 
            gamma_plus = beta + sqrt(beta*beta - w0*w0); 
            C2 = x0/(1-(gamma_minus/gamma_plus));
    %         C1 = X0 - C2;
            C1 = x0 - C2; % replaced X0 with x0
            pos_t = C1*exp(-gamma_minus*time) + C2*exp(-gamma_plus*time); 
            vel_t = -gamma_minus*C1*exp(-gamma_minus*time) - gamma_plus*C2*exp(-gamma_plus*time);                                                                                                   
    else
            pos_t = 0;
            vel_t = 0;
    end 
    
    plot(time, pos_t)
    leg{ci} = (['Beta = ' num2str(beta)]); % legend (char)  stored in cell array

end

legend(leg); % display legend once all data is plotted

hold off