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"Force" derivation of Figure 1. Force diagram of a simple gravity pendulum. Consider Figure 1 on the right, which shows the forces acting on a simple pendulum. Note that the path of the pendulum sweeps out an arc of a circle. The angle θ is measured in radians, and this is crucial for this formula.
The pendulum carries an amount of air with it as it swings, and the mass of this air increases the inertia of the pendulum, again reducing the acceleration and increasing the period. This depends on both its density and shape. Viscous air resistance slows the pendulum's velocity. This has a negligible effect on the period, but dissipates energy ...
Spherical pendulum: angles and velocities. In physics, a spherical pendulum is a higher dimensional analogue of the pendulum. It consists of a mass m moving without friction on the surface of a sphere. The only forces acting on the mass are the reaction from the sphere and gravity.
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 ...
Figure two (a)—Equatorial pendulum with longitudinal swing. For the equatorial pendulum with a swing in the latitudinal direction (along the equator) the surface velocity vectors on either side of the swing are not balanced in the same direction but are acting within the same x-y plane as the pendulum swing (see Figure 2B). These vectors are ...
A mass m attached to a spring of spring constant k exhibits simple harmonic motion in closed space. The equation for describing the period: = shows the period of oscillation is independent of the amplitude, though in practice the amplitude should be small. The above equation is also valid in the case when an additional constant force is being ...
The phase portrait of the pendulum equation x ″ + sin x = 0.The highlighted curve shows the heteroclinic orbit from (x, x′) = (–π, 0) to (x, x′) = (π, 0).This orbit corresponds with the (rigid) pendulum starting upright, making one revolution through its lowest position, and ending upright again.
The motion of a pendulum, such as the Foucault pendulum, is typically analyzed relative to an Inertial frame of reference, approximated by the "fixed stars." [ 20 ] These stars, owing to their immense distance from Earth, exhibit negligible motion relative to one another over short timescales, making them a practical benchmark for physical ...