This force will eventually bring an oscillating system to a halt, and if it is great enough, it can actually stop oscillations before they can start.Ī weight on a spring bouncing in air will continue bouncing for quite a long time, but not forever. In simple harmonic motion, the damping force is generally proportional to the velocity of the oscillating mass, according to the State University of New York Stony Brook. These forces can include frictional forces between moving parts, air resistance or internal forces such as those in springs that tend to dissipate energy as heat. Damped harmonic motionĪll mechanical systems are subject to damping forces, which cause the amplitude of the motion to decrease over time. Nevertheless, pendulums closely approximate simple harmonic motion provided they don’t swing more than a few degrees from their resting point. Since gravity is pulling the pendulum vertically downward and not back along the arc in the opposite direction of its motion, the restoring force is a somewhat complex trigonometric function.
Another significant difference is that in the case of a pendulum, the restoring force is provided not by a spring but by gravity. However, the period of a pendulum is determined not by its mass but by its length. Simple pendulums behave much like harmonic oscillators such as springs. This is exactly the same graph as we get if we plot the position of a mass on a spring bouncing up and down in simple harmonic motion as a function of time. If we plot only the vertical position of the point as the disk turns, it produces a sinusoidal graph. Consider a point on the rim of a disk as it rotates counterclockwise at a constant rate around a horizontal axis. There is a close connection between circular motion and simple harmonic motion, according to Boston University.
(Image credit: Georgia State University) Circular motion If the displacement of the mass is plotted as a function of time, it will trace out a sinusoidal wave. A ball on a spring is the standard example of periodic motion.