Trying to graph of the relationship of the frequency and wave number of the spin wave

I've been trying to make this code into a function and gather the wave number, but how do I get the frequency and then collect the data bt changing the wave number and then graphing. Below here is the code on matlab:

% 1D spin wave in a line: LLG + damping, periodic BC, arrows, live wavelength (FFT)
clear; clc; close all;

% ---- Parameters ----
N      = 100;       % number of spins along the line
a      = 0.5;      % lattice spacing (set physical units if you want)
J      = 2.0;      % exchange coupling
alpha  = 0.03;     % damping
dt     = 0.01;     % time step
T      = 50;        % total time
steps  = round(T/dt);

% ---- Initial spins: all up + localized transverse bump to launch a wave ----
S = zeros(N,3); S(:,3) = 1;
S(N,1) = 0.5;   % small tilt at center

% Positions (a straight line along x)
x = (0:N-1)*a; y = zeros(1,N); z = zeros(1,N);

% ---- Figure ----
figure('Color','w');
axis equal; axis([min(x)-a, max(x)+a, -1.2, 1.2, -1.2, 1.2]);
xlabel('X (sites)'); ylabel('Y'); zlabel('Z'); grid on; view([45 25]);

% ---- Time evolution ----
for t = 1:steps
    S_new = S;

    % Update all spins with periodic neighbors
    for i = 2:N-1
        H_eff = J * (S(2,:));
        precession = -cross(S(1,:), H_eff);
        damping_term = alpha * cross(S(1,:), precession);
        S_new(1,:) = S(1,:) + dt * (precession + damping_term);
        S_new(1,:) = S_new(1,:) / norm(S_new(1,:));
        
        % Update last spin (only affected by spin N-1)
        H_eff = J * (S(N-1,:));
        precession = -cross(S(N,:), H_eff);
        damping_term = alpha * cross(S(N,:), precession);
        S_new(N,:) = S(N,:) + dt * (precession + damping_term);
        S_new(N,:) = S_new(N,:) / norm(S_new(N,:));
        % Effective magnetic field (exchange with neighbors)
        H_eff = J * (S(i+1,:) + S(i-1,:));
        
        % LLG equation with damping
        precession = -cross(S(i,:), H_eff);
        damping_term = alpha * cross(S(i,:), precession);
        dS = precession + damping_term;

        % Euler update
        S_new(i,:) = S(i,:) + dt * dS;

        % Renormalize to unit vector
        S_new(i,:) = S_new(i,:) / norm(S_new(i,:));
    end
    S = S_new;

    % Draw every few steps
    if mod(t,5)==0
        clf;
        quiver3(x, y, z, S(:,1)', S(:,2)', S(:,3)', 0.8, 'LineWidth', 1.5);
        xlabel('X (sites)'); ylabel('Y'); zlabel('Z');
        axis equal; axis([min(x)-a, max(x)+a, -1.2, 1.2, -1.2, 1.2]); grid on; view([45 25]);

        % --- Measure wavelength from Sx along the line via spatial FFT ---
        [lambda, k_peak] = spinwave_wavelength_fft(S(:,1), a);

        title(sprintf('1D Spin Wave (periodic, \\alpha=%.2f)  t=%.2f,  k=%.3f rad/site,  \\lambda=%.2f sites', ...
              alpha, t*dt, k_peak*a, lambda/a));
        drawnow;
    end
end

% -------- Helper: wavelength from spatial FFT of Sx --------
function [lambda, k_peak] = spinwave_wavelength_fft(Sx, a)
    if nargin < 2, a = 1; end
    N  = numel(Sx);
    s  = Sx(:) - mean(Sx);             % de-mean to avoid DC dominating
    Y  = fftshift(fft(s));
    P  = abs(Y).^2;
    %plot(P);

    % k-grid (rad per physical length)
    kgrid = fftshift(2*pi/a * ((0:N-1) - floor(N/2)) / N);

    % use nonnegative k, ignore k=0
    mask = kgrid >= 0;
    kpos = kgrid(mask); Ppos = P(mask);
    if ~isempty(kpos) && kpos(1)==0
        kpos(1) = []; Ppos(1) = [];
    end

    if isempty(Ppos)
        k_peak = NaN; lambda = NaN; return;
    end

    [~, idx] = max(Ppos);
    k_peak = kpos(idx);          % rad per unit length
    lambda = 2*pi / k_peak;      % same length units as 'a'
end

I managed to visualize the spin wave and retreive the wave length and wave number, but I'm not sure about the frequency and graphing