Pendulums(单摆、复摆及应用英文版)

momentum and conservation of
energy. • A similar principle, the propagation
of waves in solids, was used in the
Constantinesco Synchronization gear system for propeller / gun
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Introduction
Composition
•A pendulum is a weight suspended from a pivot so that it can swing freely.
Properties
•Period •amplitude
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About history
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Application
Jaw crusher（复摆颚式破碎机）
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Features and values
Fast and simple maintenance Excellent suitability
High reliability
Excellent total crushing economy
Foucault Pendulum
Introduction
• The Foucault pendulum , or Foucault's
pendulum, named after the French physicist Léon
Foucault, is a simple device conceived as an experiment to demonstrate therotation of the
Clock
Thank you!
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Equation
Now the figure shows a pendulum of mass m and length L displaced slightly from equilibrium. The gravitational force exerts a torque given by
Introduction of
Our team
David
PART 01 Introduction & history
Doreen
PART 02 Simple pendulum
Yann
PART 03 Physical pendulum
Grace
PART 04 Application of pendulum & Newton pendulum
where the torque is
and the relevant moment of inertia is that about the point of suspension. The resulting equation of motion is:
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Physical pendulum
This is identical in form to the equation for the simple pendulum and yields a period
PART 02
SLeabharlann Baidumple Pendulum
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Simple Pendulum
Definition
A simple pendulum is an idealized model consisting of a point mass (I=ml^2)suspended by a massless, unstretchable string. When the point mass is pulled to one side of its straight-down equilibrium position and released, it oscillates about the equilibrium position.
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The extending knowledge
Newton cardle
The candle in motion.
Newton's cradle five-ball system in 3D two-ball swing
Application
• The most common application is that of a desktop executive toy. Another use is as an educational physics demonstration, as an example of conservation of
Solve the equation, we can get
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Analogy
Let us make an analogy between A simple pendulum with simple harmonic motion
A simple pendulum
M=-mglsinθ M=Iβ
simple harmonic motion
• The word "pendulum" comes from the Latin word "pendulus" which means "hanging". • Early Seismometer One of the earliest pendulums was a first century seismometer devised by Chinese scientist Zhang Heng. It swayed to activate a lever after earthquakes. • Galileo's Influence Around 1602, Galileo studied pendulum properties after watching a swinging lamp in the cathedral of Pisa's domed ceiling .
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Equation
then becomes (I=ml^2)
If we solve the differential equation ,we can get
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Equation
The simplest kind of oscillation occurs when the restoring force F is directly proportional to the displacement from equilibrium x. This happens if the spring is an ideal one that obeys Hooke’s law. The constant of proportionality between F and x is the force constant k. On either side of the equilibrium position, F and x always have opposite signs. Then we can get the equation
F = -kx F = ma
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PART 03
Physical Pendulum
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Physical pendulum
Hanging objects may be made to oscillate in a manner similar to a simple pendulum. The motion can be described by "Newton's 2nd law for rotation":
Earth. While it had long been known that the Earth
rotates, the introduction of the Foucault pendulum in 1851 was the first simple proof of the rotation in an easy-to-see experiment. Today, Foucault pendulums are popular displays in science museums and universities.[1]
where the minus sign indicates that the torque tends to rotate the pendulum back toward equilibrium. The rotational analog of Newton’s law, ( for small angles , then sinθ=θ)
synchronizers on early fighter
aircraft. Synchronization gear
Invention
• The largest cradle device in the world was designed by MythBusters and consisted of five one-ton concrete and steel rebar-filled buoys suspended from a steel truss.The buoys also had a steel plate inserted in between their two halves to act as a "contact point" for transferring the energy; this cradle device did not function well. A smaller scale version constructed by them consists of five 6 inches (15 cm) chrome steel ball bearings, each weighing 33 pounds (15 kg), and is nearly as efficient as a desktop model. • The cradle device with the largest diameter collision balls on public display, was on display for more than a year in Milwaukee, Wisconsin at retail store American Science and Surplus. Each ball was an inflatable exercise ball 26 inches (66 cm) in diameter (enclosed in cage of steel rings), and was supported from the ceiling using extremely strong magnets. It was dismantled in early August 2010 due to maintenance concerns.[