Two particles, each of mass M, are hung between three identical springs. Each spring is massless and has spring constant K. Neglect gravity. The masses are connected as shown to a dashpot of negligible mass.
The dashpot exerts a force bv, where v is the relative velocity of its two ends. The force opposes the motion. Let x1 and x2 be the displacements of the two masses from equilibrium.
Find the equation of motion for each mass. (Challenge: If you can, Show that the equations of motion can be solved in terms of the new dependent variables y1=x1+x2 and y2=x1-x2. And Show that if the masses are initially at rest and mass1 is given an initial velocity vo, the motion of the masses after a sufficiently long time is x1=x2=(vo/2w)*sinwt and evaluate w.)