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Hello,

I want to include kinetic friction into the harmonic oscillator.
A small blocks is attached to a horiontal spring on a table.
Because there is kinetic friction there are two forces on the blok that we need to describe the oscillation.

First, the force that the spring exerts and second, the kinetic friction.
The kinetic friction is always opposite to the velocity but it is not proportional to velocity.

The differential equation is:

[itex]x''(t)=-kx-F_{friction}[/itex]

How can I rewrite Fore of friction to solve this equation? force of friction is not just a constant since it depends on the direction of the velocity.