A simple pendulum is a theoretical model in physics consisting of a point mass suspended from a string in a frictionless environment. Its motion is described by mathematical equations, with the swing period depending on the length of the string and gravitational force. Kinetic and potential energies are also considered, making it useful for clocks until the invention of electronic and atomic clocks.
In that branch of physics called mechanics, a simple pendulum is a mental construct or an idealized theoretical model in which a mass of point dimensions is suspended from a rod or string, itself of negligible mass, used in an environment free from friction and otherwise perfect. If the string is long and the mass moves in an arc of a few degrees under the influence of gravity, the resulting motion is both linear and harmonic. The point mass behaves as if a spring were repeatedly pulling it back and forth in a line through a central point. The line of motion of a simple pendulum serves as an axis with the point as the origin. This system is described mathematically by a series of equations that are directly related to real-world processes.
The swing period or time of a simple pendulum, operating with the restrictions mentioned above is T=2π(g/L)-1/2 – in this equation the gravitational force is represented by “g” and “L” represents the length of the rope. If the arc of motion is much more than a few degrees, the simple equation listed above – only an approximation – is no longer sufficient, and must therefore include one or more terms added from an infinite virial equation. This equation is written T=2π(g/L)-1/2(1+(1/16)θ2+(11/3072)θ4+…). Theta (θ) is the arc angle in radians. In practical application, the larger the arc, the less a real pendulum resembles a simple pendulum.
As with many mechanical systems, it is interesting to consider both kinetic and potential energies. A simple pendulum must stop and reverse at both ends of its swing. The kinetic energy reaches a minimum – zero – at these points, so in accordance with the conservation of energy, the potential energy reaches its maximum. Conversely, potential energy is minimized at the center of the swing, while kinetic energy reaches its maximum. Velocity resets at both ends, but peaks at the center point.
The mathematical consideration validates the use of the pendulum in clocks. Until 1929, the Riefler pendulum clock was still in use as the time standard in the United States. Even later it was replaced by another pendulum clock, the Shortt clock. While no longer the standard or among the most accurate watches in the world, the Shortt variety achieved the astonishingly accurate resolution of one second per year. As technology advanced, it was inevitable that the basic design idealized into a simple pendulum would be replaced by an electronic and, later, an atomic clock.
Protect your devices with Threat Protection by NordVPN
