Search results
Results from the WOW.Com Content Network
A pendulum is a body suspended from a fixed support such that it freely swings back and forth under the influence of gravity. 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 towards the equilibrium position.
Assuming no damping, the differential equation governing a simple pendulum of length , where is the local acceleration of gravity, is + = If the maximal displacement of the pendulum is small, we can use the approximation sin θ ≈ θ {\displaystyle \sin \theta \approx \theta } and instead consider the equation d 2 θ d t 2 + g l θ = 0 ...
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 presence of the acceleration of gravity g in the periodicity equation (1) for a pendulum means that the local gravitational acceleration of the Earth can be calculated from the period of a pendulum. A pendulum can therefore be used as a gravimeter to measure the local gravity, which varies by over 0.5% across the surface of the Earth. [107]
These curves correspond to the pendulum swinging periodically from side to side. If < then the curve is open, and this corresponds to the pendulum forever swinging through complete circles. In this system the separatrix is the curve that corresponds to =. It separates — hence the name — the phase space into two distinct areas, each with a ...
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 ...
Monumental conical pendulum clock by Farcot, 1878. A conical pendulum consists of a weight (or bob) fixed on the end of a string or rod suspended from a pivot.Its construction is similar to an ordinary pendulum; however, instead of swinging back and forth along a circular arc, the bob of a conical pendulum moves at a constant speed in a circle or ellipse with the string (or rod) tracing out a ...
Classical mechanics utilises many equations—as well as other mathematical concepts—which relate various physical quantities to one another. These include differential equations, manifolds, Lie groups, and ergodic theory. [4] This article gives a summary of the most important of these.