Consider a mass

between two springs attached to opposing walls. Let

and

be the respective spring constants. A displacement of the mass by a distance

results in the first spring lengthening by

, while the second spring is compressed by

(and pushes in the same direction). Suppose that the equilibrium position is at

, where the two springs have their force-free lengths. The equation of motion is then given by

, where

is the viscous damping coefficient in

and

is the natural frequency of the system. Evidently, the two springs are dynamically equivalent to a single spring with constant

. The solution is

. When

(no damping), this reduces to

. The motion is traced by the red curves in the right panel.