The applet shows the motion of a point along a vertical (one-dimensional) line. [br][list][*]Notice that the (instantaneous) position, velocity, and acceleration of the point are given.[/*][*]Use the slider tool or input box to move the point P to a specific time value. [/*][*]Use the check boxes to show/hide the tangent line, graph of [math]f'(x)[/math], and graph of [math]f''(x)[/math]. [br][/*][/list]

[b]Oscillations with Dampening: [/b]The standard example of this type of motion is a mass attached to the end of a spring with friction. If you move the mass and stretch the spring, it will pull the mass back toward equilibrium but because of its momentum it will move past equilibrium to the other side until the spring compresses enough and begins pushing the mass back the other way. However, unlike with simple harmonic oscillators, if we assume there is friction (or some other force that causes a loss of energy), then the mass will not quite reach the position is started at. Over time the energy loss will cause the oscillations to get smaller and smaller until the mass settles at the equilibrium position of the spring.