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An important concept is the equivalent length, , the length of a simple pendulums that has the same angular frequency as the compound pendulum: =:= = Consider the following cases: The simple pendulum is the special case where all the mass is located at the bob swinging at a distance ℓ {\displaystyle \ell } from the pivot.
"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 equilibrium position.
Rayleigh–Lorentz pendulum (or Lorentz pendulum) is a simple pendulum, but subjected to a slowly varying frequency due to an external action (frequency is varied by varying the pendulum length), named after Lord Rayleigh and Hendrik Lorentz. [1] This problem formed the basis for the concept of adiabatic invariants in mechanics. On account of ...
A seconds pendulum is a pendulum whose period is precisely two seconds; one second for a swing in one direction and one second for the return swing, a frequency of 0.5 Hz. [ 1 ] Pendulum
A simple pendulum that has the same natural frequency as a compound pendulum defines the length from the pivot to a point called the center of oscillation of the compound pendulum. This point also corresponds to the center of percussion .
Other phenomena can be modeled by simple harmonic motion, including the motion of a simple pendulum, although for it to be an accurate model, the net force on the object at the end of the pendulum must be proportional to the displacement (and even so, it is only a good approximation when the angle of the swing is small; see small-angle ...
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A simple pendulum with oscillating pivot point. The situation changes if the pivot point is moving, e.g. undergoing a simple harmonic motion = , where is the amplitude, the angular frequency, and time.