![]() ![]() 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. ![]()
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