This Demonstration shows a system with two masses,

and

. Let

and

be the positions of the masses,

and

be the lengths of the springs, and

and

be the spring constants. The effect of the damper can be represented by a damping coefficient

in the system. The energy decreases whenever the second mass is moving relative to the first. It is said that the damper is "tuned" when the optimal value of

is selected for a specific building. Hamilton's equations of motion are solved for the initial conditions

and

(positions and momenta). Their plots are shown for all three possible combinations of three variables. Below the plot, the state of the masses with the springs and the damper is shown as a function of time.