How to use ODE45 to solve 2nd order differential equation with random variables in it?

In Quarter car model equations, (see above attached file for skematic model)

where

= sprung mass

= unsprung mass

= non- linear spring stifffness

= linear spring stiffness

= linera damper of damping coefficient

- Sinusodial function with Amplitude and frequency

are independent random variables with normal distribution.

how could i apply this random variables to the equations by using ode45 ?

I have done for one sample, any hint to simulate for 100 samples.

dt = 0.01;
tf = 30;
tspan = dt:dt:tf;

y0 = [0;100;0;10];
[t,y] = ode45('eqsystem',tspan,y0);

plot(y(:,1))
grid
xlabel('X-Displacement')
ylabel('y-Displacement')
title('X vs Y Displacement')

hold on;

function dydt = eqsystem(t,y)

ks = 1000;      % N/m^3 - Gaussian
ku = 1000;      % N/m - Gaussian
ms = 10;        % kg - Gaussian
mu = 20;        % kg - Gaussian
c = 300;        % Ns/m - Gaussian
A = 0.10;       % m -
omega = 2*pi;   % rad/s -

dydt = zeros(4,1);

dydt(1,:) = y(2);

dydt(2,:) = ((-ks/ms)* (y(1)-y(3))^3 - (c/ms)*(y(2)-y(4)));

dydt(3,:) = y(4);

dydt(4,:) = ((ks/mu)*(y(1)-y(3))^3 + (y(2)-y(4)) + ku*(A*sin(omega*t) - y(3)));

end

[Jan]

What does e.g. "(10,1)" mean? Normaly distributed around 10 withd std 1?

[RAJESH M]

(mean,standard deviation) = (10,1)

Answer 1

[Jan]

dt = 0.01;
tf = 30;
tspan = dt:dt:tf;
y0 = [0;100;0;10];

for k = 1:100
   ms = 10 + randn;
   mu = 20 + randn * 2;
   ...
   fcn = @(t, y) eqsystem(t, y, ms, mu, ...)
   [t, y] = ode45('eqsystem',tspan,y0);
end

function dydt = eqsystem(t, y, ms, mu, ...)
dydt    = zeros(4,1);
dydt(1) = y(2);
dydt(2) = (-ks / ms) * (y(1) - y(3))^3 - (c/ms) * (y(2) - y(4));
dydt(3) = y(4);
dydt(4) = (ks / mu) * (y(1) - y(3))^3 + (y(2) - y(4)) + ...
          ku * (A * sin(omega * t) - y(3));
end

[RAJESH M]

Thank you very much.