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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.
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]
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 ...
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 ...
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.
In advanced classical mechanics it is often useful, and in quantum mechanics frequently essential, to express Maxwell's equations in a potential formulation involving the electric potential (also called scalar potential) φ, and the magnetic potential (a vector potential) A. For example, the analysis of radio antennas makes full use of Maxwell ...
A Wilberforce pendulum, invented by British physicist Lionel Robert Wilberforce around 1896, [1] consists of a mass suspended by a long helical spring and free to turn on its vertical axis, twisting the spring. It is an example of a coupled mechanical oscillator, often used as a demonstration in physics education.
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