Hi,
I understand that you are facing difficulties in writing the equations for a spring mass system.
The code snippet provided simulates the position and velocity of a spring-mass system using Euler method for numerical integration.
Below is the refactored code snippet. You can review each section and the plots. I have added comments to explain each section for better understanding.
t_total = 10; % total integration time (s)
dt = 0.01; % integration time step (s)
% System parameters
m_c = 1; % container mass in kg
k_s1 = 10; % spring constant of s1 in N/m
k_s2 = 10; % spring constant of s2 in N/m
d = 0; % gap in meters (not used in this version)
g = 9.8; % gravitational acceleration in m/s^2 (not used in this version)
% Initialize variables
t = 0:dt:t_total; % time array
x_new = zeros(2, length(t)); % position and velocity array
% Initial conditions
x_new(:, 1) = [0; 1]; % initial position and velocity
% loop to update the position and velocity at each time step
for i = 2:length(t)
x = x_new(:, i-1); % current position and velocity
x_delta = [x(2); -(k_s1/m_c) * x(1) - (k_s2/m_c) * x(1) - (c/m_c) * x(2)] * dt; % change in position and velocity based on system dynamics
x_new(:, i) = x + x_delta; % update position and velocity
end
% Plot the velocity-time graph
figure();
plot(t, x_new(2, :));
title('Velocity-time Response');
xlabel('Time (s)');
ylabel('Velocity (m/s)');
Here is a breakdown of the code:
- To provide you the plot results, I have assigned system parameters (m, k, c, t_total, dt) to some values
- Create a time array (t) from 0 to t_total with a step size of dt. Also create an array (x_new) to store position and velocity values
- Assign initial position and velocity to the first element of x_new
- Perform numerical integration using the Euler method
- Plot the position-time and velocity-time graphs, respectively
I hope this revised code snippet is helpful to you.
