How to plot upper and lower bounds in graph with 95% confidence.

% preallocate output variables
n_files = 2;
Time = cell(n_files, 1);
Veloc = cell(n_files, 1);
Ypk_plot = cell(n_files, 1);
Xpk_plot = cell(n_files, 1);
Y = cell(n_files, 1);
X = cell(n_files, 1);
P = cell(n_files, 1);
damp_ratio = zeros(1, n_files);
wd = zeros(1, n_files);
wn = zeros(1, n_files);
K_ex = zeros(1, n_files);

% read Data from files and process each file
for j = 1:n_files
    % read Data from file
    z1 = importdata("Xxsv0000"+num2str(j)+".txt");

    % extract time and velocity Data
    Time{j} = z1.data(:,1);
    Veloc{j} = z1.data(:,2);
    
    % find local maxima in velocity Data within the range of indices
    [Ypk, Xpk] = findpeaks(Veloc{j}(1:550));
    Ypk_plot{j} = Ypk(11:35);
    Xpk_plot{j} = Xpk(11:35);
    Y{j} = Ypk;
    X{j} = Xpk;
    P{j} = zeros(size(Ypk));

    % plot Data against time Data and mark the locations of the peaks found
    figure
    plot(Time{j}, Veloc{j}, 'DisplayName', 'Data')
    hold on
    plot(Time{j}(Xpk_plot{j}), Ypk_plot{j}, 'dr', 'DisplayName', 'Pick points')
    grid on
    legend('Data','Pick Points','FontSize',12)
    xlabel('Time','FontSize',12)
    ylabel("Voltage (V/V)",'FontSize',12)
    sgtitle(['K', num2str(j)])

    % calculate logarithmic decrement, damping ratio, and natural frequency
    t_new = Time{j}(X{j});
    y_new = Y{j};
    Log_Dec = abs(log(y_new(1:end-1) ./ y_new(2:end)));
    Mean_dec = mean(Log_Dec);
    Damp_period = (t_new(end) - t_new(1)) / length(t_new);
    wd(j) = 2*pi / Damp_period;
    damp_ratio(j) = Mean_dec / sqrt((2*pi)^2 + Mean_dec^2);
    wn(j) = wd(j) * sqrt(1 - damp_ratio(j)^2);

    % calculate spring constant
     
    K_ex(1,j) = m_for_k(1,j) * wn(1,j)^2;
end
clear j n_files  t_new Time Veloc X Xpk Xpk_plot Y;
clear y_new Ypk_plot z1  Damp_period Log_Dec Mean_dec Ypk P;

Answer 1

[Walter Roberson]

For this type of task, plotting 95% confidence, a common technique is to take the standard deviation std and use norminv to find the 2.5% and 97.5% probability levels for that mean and standard deviation, and plot those