If we consider a block of mass m attached to a spring, where the system oscillates on a table with friction f, the friction force f on the block would depend on the direction of the velocity, as(adsbygoogle = window.adsbygoogle || []).push({});

[tex] m\ddot{x} = \begin{cases} -kx+f & \text{if } \dot{x}<0\\ -kx-f & \text{if } \dot{x} > 0 \end{cases}[/tex]

If I just look at one equation at a time and solve them both separatly first, I get equations where the amplitude doesn't drop with time. But that should be the case (energy in that closed system isn't conserved). So how can I solve this system?

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# Constant damping force on springsystem

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