Thank you very much for helping everyone who contributed!

@Tom68 

For better undestanding my problem, I provide a schematic diagram of investigated mechanism.

It is basically a piston in a cylinder that hangs on a spring.
The friction is caused by the piston seal and I measured it on real mechanism (I know, the friction value is smaller by moving compare to the start).

G=mg is initialize force by condition (spring lenth = l) mentioned in my last post. How to bring it to the equation in Maple?

Many thanks in advance.

@vv 

Many Thanks! Tomas

@Preben Alsholm 

Dear Mr. Alsholm,

many thanks for your solution! It´s simple and functional! I have tried to use the command signum during my tests as well but without numerical solution...

I have another question - how to add to the final graph a second curve of velocity? My command:

>plots [odeplot] (res,[[t,x(t)],[t,D(t)]],t=0..10,numpoits=500];

makes only curve of x(t)....

And last question - how to bring to the equation an initialize force? I.e. force of first spring activation?

m*diff(x(t),t,t) + k*x(t) + mu*m*g*signum(v(t)) = F  ???

Thank you a lot for once again for you help!

Tomas