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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.
Snap, [6] or jounce, [2] is the fourth derivative of the position vector with respect to time, or the rate of change of the jerk with respect to time. [4] Equivalently, it is the second derivative of acceleration or the third derivative of velocity, and is defined by any of the following equivalent expressions: = ȷ = = =.
"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.
The period of a mass attached to a pendulum of length l with gravitational acceleration is given by = This shows that the period of oscillation is independent of the amplitude and mass of the pendulum but not of the acceleration due to gravity, g {\displaystyle g} , therefore a pendulum of the same length on the Moon would swing more slowly due ...
There are two main descriptions of motion: dynamics and kinematics.Dynamics is general, since the momenta, forces and energy of the particles are taken into account. In this instance, sometimes the term dynamics refers to the differential equations that the system satisfies (e.g., Newton's second law or Euler–Lagrange equations), and sometimes to the solutions to those equations.
The time for one complete cycle, a left swing and a right swing, is called the period. The period depends on the length of the pendulum, and also to a slight degree on its weight distribution (the moment of inertia about its own center of mass) and the amplitude (width) of the pendulum's swing.
The true acceleration at time t is found in the limit as time interval Δt → 0 of Δv/Δt. An object's average acceleration over a period of time is its change in velocity, , divided by the duration of the period, .
In Cavendish's time, physicists used the same units for mass and weight, in effect taking g as a standard acceleration. Then, since R earth was known, ρ earth played the role of an inverse gravitational constant.