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.
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]
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 ...
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 ...
A pendulum can be used to measure the acceleration of gravity g because for narrow swings its period of swing T depends only on g and its length L: [2] = So by measuring the length L and period T of a pendulum, g can be calculated.
The equations of motion describe the movement of the center of mass of a body, ... The acceleration is the time derivative of the velocity: () ... Pendulum (mechanics)
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 ...
By considering limit cases, the correctness of this system can be verified: For example, ¨ should give the equations of motion for a simple pendulum that is at rest in some inertial frame, while ¨ should give the equations for a pendulum in a constantly accelerating system, etc.