My index starts at the second element. I dont know why

Below I have attached the code. I am trying to write a script to plot the responses of three different damping ratios on a single degree of freedom system. To me the code looks write with maybe a few errors. However the error I am constantly running into is that even though I have set i = 1, once my for loop starts i becomes = 2. Until the line for i = 1:length(d_ratio), i = 1. i have tested this. But once the for loop starts its first iteration it wont run due the index starting at 2. If someone could explain to me what I am missing that would appreciated.

Given values

% Given Values
d_ratio = [0.05,0.1,0.2]; % Damping Ratios
w_n = 5; % Damped Angular Frequency

% Initial Values
t = 0; % Time
v = 60; % Velocity
x = 0; % Displacement
i=1; t(i)=0; v(i)=60; x(i)=0;

% Acceleration Values (constant)
w_d = sqrt(1 - (d_ratio.^2 * w_n)); % Acceleration equation. Gives a value of acceleration for each ratio value. These values stay constant

% Time Values
h = 0.01; % Time step
total_t = 7; % Total period of time
time_array = 0:h:total_t; % An array which holds all time steps of 0.01 from 0 to 7 seconds

For Loop

for i = 1:length(d_ratio) % index = 3 values of array d_ratio, starting at the first element
    
    C = sqrt(x(i)^2) + ((d_ratio*w_n*x(i)+v(i))/(w_d)); % Amplitude equation
    phase = atan2((d_ratio*w_n*x(i)+v(i)), (w_d*x(i))); % Phase equation
    
    x = C*exp(-d_ratio*w_n*t(i)).*cos(w_d*t(i)-phase); % System response equation
    
    % Plotting the responses for the ratios 0.05, 0.1, 0.2
    plot(t,x);
    hold on;
end

Plot Formatting

xlabel('time (s)');
ylabel('displacement (cm)');
title('Response of the System for the Damping Ratios: 0.05, 0.1, 0.2');
grid on;
hold off;

Answer 1

[Torsten]

Before MATLAB enters the for-loop, t(i), v(i) and x(i) are only defined for i = 1. In the loop, you also don't define t(i), v(i) and x(i) for i>1. This will make MATLAB error for the second loop index (i=2).