Mass between Two Damped Springs

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.


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