Can someone explain this piece of code:

I'm very new to Matlab and coding in general and I have to write a program for a spring mass system.

I'm having trouble writing the equations out in Matlab form...

m_c=m_c; % container mass in kg
k_s1=k_s1; % spring constant of s1 in N/m
k_s2=k_s2; % spring constant of s2 in N/m
c=c; % damping coefficient in Ns/m
d=d; % gap in metres
t_total=t_total; % total integration time in seconds
dt=dt; % integration step in seconds
g=9.8; % gravitational acceleration in m/s^2
function[t,x_new]=Massspringdamper(m_c,c,k_s1,k_s2,t_total,dt);
t=0:dt:t_total;
x_new(:,1)=x_start;
for i=2:length(t)



x_delta=[0,1;-k_s1/m_c,-c/m_c]*x_new(:,i-1)*dt;
x_new(:,i)=x_new(:,i-1)+x_delta;
end


% figure()
% plot(t, x_new(1,:), 'o')
% title('Position-time')
% xlabel('time')
% ylabel('position')

[t,x_new]=Massspringdamper(m_c,c,k_s1,k_s2,t_total,dt);   
figure()
plot(t, x_new(2,:), 'o')
title('Velocity-time Response')
xlabel('time')
ylabel('velocity')

Answer 1

[Harshavardhan Putta]

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.