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Figure 3. Deviation of the "true" period of a pendulum from the small-angle approximation of the period. "True" value was obtained numerically evaluating the elliptic integral. Figure 4. Relative errors using the power series for the period. Figure 5. Potential energy and phase portrait of a simple pendulum.
Pendulum. "Simple gravity pendulum" model assumes no friction or air resistance. A pendulum is a device made of a weight suspended from a pivot so that it can swing freely. [1] When a pendulum is displaced sideways from its resting, equilibrium position, it is subject to a restoring force due to gravity that will accelerate it back toward the ...
The loaded swing, a pendulum, has a natural frequency of oscillation, its resonant frequency, and resists being pushed at a faster or slower rate. A familiar example is a playground swing, which acts as a pendulum. Pushing a person in a swing in time with the natural interval of the swing (its resonant frequency) makes the swing go higher and ...
Because the latitude of its location was = ′, the plane of the pendulum's swing made a full circle in approximately ′ (), rotating clockwise approximately 11.3° per hour. The proper period of the pendulum was approximately /, so with each oscillation, the pendulum rotates by about . Foucault reported observing 2.3 mm of deflection on ...
Mechanical resonance. Mechanical resonance is the tendency of a mechanical system to respond at greater amplitude when the frequency of its oscillations matches the system's natural frequency of vibration (its resonance frequency or resonant frequency) closer than it does other frequencies. It may cause violent swaying motions and potentially ...
Double pendulum. A double pendulum consists of two pendulums attached end to end. In physics and mathematics, in the area of dynamical systems, a double pendulum also known as a chaotic pendulum is a pendulum with another pendulum attached to its end, forming a simple physical system that exhibits rich dynamic behavior with a strong sensitivity ...
A net restoring force then slows it down until its velocity reaches zero, whereupon it is accelerated back to the equilibrium position again. As long as the system has no energy loss, the mass continues to oscillate. Thus simple harmonic motion is a type of periodic motion. If energy is lost in the system, then the mass exhibits damped oscillation.
The main advantage of this type of pendulum is its low energy use; with a period of 12–15 seconds, compared to the gravity swing pendulum's period of 0.5—2s, it is possible to make clocks that need to be wound only every 30 days, or even only once a year or more.