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The animations below depict the motion of a simple (frictionless) pendulum with increasing amounts of initial displacement of the bob, or equivalently increasing initial velocity. The small graph above each pendulum is the corresponding phase plane diagram; the horizontal axis is displacement and the vertical axis is velocity. With a large ...
"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.
A simple pendulum exhibits approximately simple harmonic motion under the conditions of no damping and small amplitude. Assuming no damping, the differential equation governing a simple pendulum of length l {\displaystyle l} , where g {\displaystyle g} is the local acceleration of gravity , is d 2 θ d t 2 + g l sin θ = 0. {\displaystyle ...
Other phenomena can be modeled by simple harmonic motion, including the motion of a simple pendulum, although for it to be an accurate model, the net force on the object at the end of the pendulum must be proportional to the displacement (and even so, it is only a good approximation when the angle of the swing is small; see small-angle ...
For example, an experimental uncertainty analysis of an undergraduate physics lab experiment in which a pendulum can estimate the value of the local gravitational acceleration constant g. The relevant equation [1] for an idealized simple pendulum is, approximately,
The seconds pendulum (also called the Royal pendulum), 0.994 m (39.1 in) long, in which each swing takes one second, became widely used in quality clocks. The long narrow clocks built around these pendulums, first made by William Clement around 1680, became known as grandfather clocks. The increased accuracy resulting from these developments ...
Effects of a blow on a hanging beam. CP is the Center of Percussion, and CM is the Center of Mass of the beam. Imagine a rigid beam suspended from a wire by a fixture that can slide freely along the wire at point P, as shown in the Figure.
Simple pendulum. Since the rod is rigid, the position of the bob is constrained according to the equation f(x, y) = 0, the constraint force C is the tension in the rod. Again the non-constraint force N in this case is gravity. Newton's laws and the concept of forces are the usual starting point for teaching about mechanical systems. [5]