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The real period is, of course, the time it takes the pendulum to go through one full cycle. Paul Appell pointed out a physical interpretation of the imaginary period: [16] if θ 0 is the maximum angle of one pendulum and 180° − θ 0 is the maximum angle of another, then the real period of each is the magnitude of the imaginary period of the ...
Gravimeter with variant of Repsold–Bessel pendulum An Autograv CG-5 gravimeter being operated. A gravimeter is an instrument used to measure gravitational acceleration. Every mass has an associated gravitational potential. The gradient of this potential is a force. A gravimeter measures this gravitational force.
Gulf gravimeter: One of the last and most accurate pendulum gravimeters was the apparatus developed in 1929 by the Gulf Research and Development Co. [124] [125] It used two pendulums made of fused quartz, each 10.7 inches (270 mm) in length with a period of 0.89 second, swinging on pyrex knife edge pivots, 180° out of phase. They were mounted ...
In physics and mathematics, in the area of dynamical systems, an elastic pendulum [1] [2] (also called spring pendulum [3] [4] or swinging spring) is a physical system where a piece of mass is connected to a spring so that the resulting motion contains elements of both a simple pendulum and a one-dimensional spring-mass system. [2]
The pendulum had two of these knife blade pivots (a), facing one another, about a meter (40 in) apart, so that a swing of the pendulum took approximately one second when hung from each pivot. Kater found that making one of the pivots adjustable caused inaccuracies, making it hard to keep the axis of both pivots precisely parallel.
This equation resembles the simple nonlinear pendulum equation, because it can swing through the vertical axis, with an additional term to account for the rotation about the vertical axis (the constant a is related to the angular momentum p φ). Applying the Lagrangian approach there are two nonlinear coupled equations to solve. The θ equation is
The quantum pendulum is fundamental in understanding hindered internal rotations in chemistry, quantum features of scattering atoms, as well as numerous other quantum phenomena. Though a pendulum not subject to the small-angle approximation has an inherent nonlinearity, the Schrödinger equation for the quantized system can be solved relatively ...
A Wilberforce pendulum can be designed by approximately equating the frequency of harmonic oscillations of the spring-mass oscillator f T, which is dependent on the spring constant k of the spring and the mass m of the system, and the frequency of the rotating oscillator f R, which is dependent on the moment of inertia I and the torsional ...