If you follow the Simulink block, you can write the equation of a simple mass-spring-damper system connected in a series like this (here is supposed m=1 for simplicity)
similarly, you can write the equation for any other nonlinear damper model. The 2nd order ODE is equivalent to the following system of first-order ODEs
Now you can write ode45 to solve this system
b1 = 1;
b2 = 0.5;
b3 = 0.1;
b4 = 0.01;
b5 = 0.001;
k = 2;
odeFun = @(t,y) [y(2); -b1*y(2)-sign(y(2))-b2*y(2)^2-b3*y(2)^3-sign(y(2))*b4*y(2)^4-b5*y(2)^5-k*y(1)];
tspan = [0 5];
ic = [1; 0];
[t,y] = ode45(odeFun, tspan, ic);
plot(t,y);
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