I'm confused finding a solution (numerical integration is ok) for the following model:(adsbygoogle = window.adsbygoogle || []).push({});

http://imageshack.com/a/img27/7080/brmb.jpg [Broken]

Free body diagrams:

http://imageshack.com/a/img22/9523/r0is.jpg [Broken]

And the equations of motion:

\begin{align}

k_{s,1}x_1+k_{s,2}x_1^3+k_m(x_1-x_2)+k_f(x_1-x_3) &= F\\

d_m\dot{x}_2-k_m(x_1-x_2) &= 0\\

F_fsign(\dot{x}_3)-k_f(x_1-x_3) &= 0

\end{align}

How can I solve these equations, preferably using a ODE solver. Problem is the lack of first derivatives. Substitution is possible when the lowest element is not present. But with this system I cannot find a solution. Help appreciated!

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# Solution for mixed differential and algebraic equations

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