@Disla , thanks , of course your right, first I solved the equation where spring & damper were attached to each other and then I was got too sleepy when I split the distance into L1 & L2 
One of the possible applications of the model is Tunned mass dampers like the one in the Taipei 101 skyscraper. I added one to a steel tower to find the big difference under seismic actions.Very cool.
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