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Topic: Periodic motion

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	Periodic Motion - The Pendulum
		Downers Grove IL 60516 Joliet IL 60435 (708) 964-6603 (815) 727-6950 Objectives: To introduce the concept of periodic motion and relate it to the movement of a pendulum.
		To discover that the period of a pendulum is dependent on the length of the pendulum and independent of the bob and the amplitude.
		By using this self graphing technique, it is not necessary for the students to measure the pendulum's length and the effect of the length of the pendulum on the period is shown quite dramatically.
	www.iit.edu /~smile/ph93dl.html (875 words)

	Periodic Motion
		A particular kind of periodic motion is known as simple harmonic motion.
		An interesting and important characteristic of all simple harmonic motion is that the period remains the same even for motions with quite different amplitudes.
		Circular motion is another example of motion whose period is independent of the amplitude.
	www.ux1.eiu.edu /~cfadd/1350/13Oscill/SHM.html (441 words)

	Periodic Motion - Succeed in Physical Science
		This is called periodic motion and can be seen in such examples of a weight on a string and seen how it swinging back and forth or a ball will bouncing up and down.
		Another use for the knowledge of periodic motion is that it applies to the study of wave motion, including light, sound, and music.
		Velocity, period, and amplitude are common characteristics of periodic motion.
	www.school-for-champions.com /science/periodic.htm (804 words)

	Literature Survey – Detection of Cyclic Motion using Computer Vision (Site not responding. Last check: 2007-10-12)
		This literature survey examines three recent papers on the subject of detecting and quantifying 3D periodic motion of an object seen in image sequences.
		The authors define “cyclic motions” which is different from “periodic motions”, and then try to determine information about motion irregularities by adopting the notion of the instantaneous period.
		The authors Polana and Nelson in [2] define methods for detection of periodic, nonrigid motion and further explore methods for using this information for recognition of types of motion, such as a human walking, a human running, and the motion of a toy frog.
	www.stanford.edu /~aplotnik/cs223b/lit_survey.htm (1928 words)

	... DSP by Richard G Baldwin
		The motion of the bag causes the sand to be leaked in a back-and-forth zigzag pattern.
		The motion of the carpet causes that pattern to be elongated along the horizontal axis.
		The kind of motion exhibited by a simple pendulum is often referred to as periodic motion in general, and simple harmonic motion in particular.
	www.dickbaldwin.com /dsp/Dsp00100.htm (3582 words)

	MOTION IN TWO DIMENSIONS (Site not responding. Last check: 2007-10-12)
		Motion information is given allowing one to calculate to speed and angle with which the object leaves the edge of the cliff.
		periodic motion where the unbalanced force varies directly with the displacement from the equilibrium point; this motion is described by the period, the frequency, and the amplitude of the motion
		The period of a simple harmonic oscillator is dependent upon the spring constant and the mass that is oscillating.
	www.ship.edu /~sagoul/motion_in_two_dimensions.htm (3524 words)

	motion Comparison Table (Site not responding. Last check: 2007-10-12)
		For orbital motion in the solar system, motion that is counterclockwise in the orbit as seen from the north pole of the ecliptic; for an object observed on the celestial sphere, motion that is from west to east, resulting from the relative motion of the object and the Earth.
		Motion in the same direction as the prevailing direction of motion.
		Apparent motion of a planet in a direction opposite to its normal progress across the sky produced by the orbital motion of the earth.
	www.site.uottawa.ca:4321 /astronomy/motion_table.html (326 words)

	PHYS1000: Periodic motion (Site not responding. Last check: 2007-10-12)
		For periodic motion, the time it takes for the motion to repeat itself (the period T) is one of the important ways we can measure the motion.
		How often the motion repeats itself in a given time (the frequency) is also useful.
		For uniform circular motion, the period is related to the radius and speed:
	www.physics.uq.edu.au /course_archive/phys1000/periodic.html (279 words)

	Periodic function - Wikipedia, the free encyclopedia
		In mathematics, a periodic function is a function that repeats its values after some definite period has been added to its independent variable.
		Periodic motion is motion in which the position(s) of the system are expressible as periodic functions, all with the same period.
		an infinite image is given by the color as function of position, the periodicity of the function corresponds to translational symmetry of the object.
	en.wikipedia.org /wiki/Periodic_function (622 words)

	Physics 128 Lecture: Periodic Motion
		The common back-and-forth motion of a pendulum or a repeated steps of a dancer are examples of this type of movement.
		Periodic motion is characterized by a period, T, that is the amount of time needed to make one complete cycle.
		The motion can also be described by frequency, f, which is the number of cycles that take place during a given unit of time.
	www.cord.edu /dept/physics/p128/lecture98_30.html (948 words)

	Periodic motion detection and classification
		an object’s motion is periodic is a strong cue for object and action recognition.
		We analyze the periodicity of a moving object using image similarities of a tracked object.
		While each system is periodic, each has qualitatively different types of periodicities, which is shown in their respective similarity plots an autocorrelations.
	research.microsoft.com /~rcutler/periodic/periodic_motion.htm (779 words)

	Week12-1.doc - Title
		The general equation for simple harmonic motion along the x-axis results from a straightforward application of Newton's second law to a particle of mass m acted on by a force F = -kx, where x is the displacement from equilibrium.
		Viewed edge-on (i.e., projected along a diameter) the motion of a particle moving uniformly with angular speed in a circle of radius A is indistinguishable from a particle oscillating harmonically in one dimension with amplitude A and angular frequency.
		Harmonic motion can be analyzed in terms of a particle with a fixed total energy oscillating in a potential-energy "well," i.e., in the presence of a potential that increases in either direction away from the equilibrium point.
	www.physics.csbsju.edu /RPEG/rtf/Lesson.11.A.html (2937 words)

	Untitled Document
		As we shall see, the displacement of a particle in periodic motion can always be expressed in terms of sines and cosines.
		Some examples are the oscillations of the balance wheel of a watch, a violin string, a mass attached to a spring, atoms in molecules or in a solid lattice, and air molecules as a sound wave passes by.
		Although we cannot eliminate friction from the periodic motions of gross objects, we can often cancel out its damping effect by feeding energy into the oscillating system so as to compensate for the energy dissipated by friction.
	www.aiaa.org /tc/sd/Education/physics_of_sd/experiments/Oscillation (658 words)

	#1 Site For Learning Science
		Linear motion is the easiest motion to study and we have seen how equations of motion can be used to calculate velocities, displacements and accelerations.
		In circular motion, a body is under a central force (centripetal force) which is constant in magnitude.
		A linear simple harmonic motion can be defined as the linear periodic motion of a body, where the restoring force is directed towards the mean position and its magnitude is proportional to the displacement from the mean position.
	home.att.net /~cat4a/shm-I.htm (682 words)

	SHM FAQs (Site not responding. Last check: 2007-10-12)
		Periodic motion is any motion that repeats itself in equal intervals of time.
		The motion of a pendulum, for small oscillations, or a mass on a spring is also an example of simple harmonic motion.
		A is the amplitude of the motion, the constant w is 2p times the frequency, and the constant f simply shifts the motion forward or backward in time and is called the phase.
	acad.udallas.edu /physics/GP1/faqs_shm.htm (1528 words)

	What are the characteristics of sound waves? (Site not responding. Last check: 2007-10-12)
		Periodic motion is classically demonstrated by the up and down motion of a dropped weight (mass) attached to a spring or by observing the motion of a pendulum.
		Periodic motion depends on two prime factors; 1) elasticity, in that medium being distorted return to its original state (equilibrium), and 2) a source of energy to initiate and sustain motion.
		Simple harmonic motion, the motion described by mass/spring example above, is represented in sound as a sine wave, which traces the mathematical shape of it namesake.
	www.indiana.edu /~emusic/acoustics/waves.htm (358 words)

	Dr. Michael A. Rudzsky's Home Page
		We show how periodic motions can be represented by a small number of eigenshapes that capture the whole dynamic mechanism of the motion.
		Thus, one motion period, like a step of a walking man or a rabbit hop, can be used as a natural unit of motion.
		The period can also be estimated in a straightforward manner by looking for the frame where the external object contour best matches the object contour in the current frame.
	www.cs.technion.ac.il /~rudzsky/mobacl2.htm (1919 words)

	Periodic Motion (Site not responding. Last check: 2007-10-12)
		In atomic time, the second is defined by a certain number of periods, cycles, of microwave radiation needed to raise the energy of a particular cesium isotope from its lowest to next highest state.
		To describe wave motion in a more quantitative manner, we can specify parameters which are always present in the wave’s periodic motion.
		Perturbations in the orientation of the earth’s axis makes the periodicity of the rotation and revolution of the earth vary ever so slightly so that time keeping or frequency counting is more precise using the cesium isotope laser.
	www.mste.uiuc.edu /courses/ci430fa00/school/4/measurement/periodic.htm (347 words)

	Spectral Signatures
		The spectral signatures for periodic, quasiperiodic, and chaotic motion are illustrated in Figure 3.26.
		In periodic motion, all the peaks are rationally related to the primary peak (resonance).
		Quasiperiodic motion is characterized by the coexistence of two incommensurate frequencies.
	cnls.lanl.gov /~nbt/Book/node92.html (413 words)

	General Wave Motion - Succeed in Physical Science
		All waves have similar characteristics, and since all forms of wave motion follow the same laws and principles, knowing the fundamentals of wave motion is important in understanding sound, light, and other types of waves.
		Wave motion is defined as the movement of a distortion of a material or medium, where the individual parts or elements of the material only move back-and-forth, up-and-down, or in a cyclical pattern.
		Although light is classified as a transverse wave, the motion of the electrical and magnetic fields may be circular instead.
	www.school-for-champions.com /science/waves.htm (1049 words)

	Mathwords: Periodic Motion
		Motion that repeats itself identically over and over, such as the swinging of a pendulum.
		If the motion can be modeled using a sinusoid it is called simple harmonic motion.
		Period of periodic motion, frequency of periodic motion, periodic function
	www.mathwords.com /p/periodic_motion.htm (49 words)

	Chapter 6 Projectile and Periodic Motion
		Suppose a ball was thrown horizontally at the velocity of 5 m/s.
		A projectile motion, since it doesn't repeat, is not periodic.
		The motion of a swinging ball is an example of circular motion.
	library.thinkquest.org /10796/ch6/ch6.htm (882 words)

	Periodic Motion Information (Site not responding. Last check: 2007-10-12)
		For instance, most human locomotory motions (e.g., walking running, skipping, shuffling) are periodic in a frame of reference that moves with the person.
		The period trace is shown superimposed on the error surface from which it was recovered.
		Real repeating motions tend not to be perfectly even, i.e., the period varies slightly from one cycle to the next, because of physically important changes in the scene.
	www-2.cs.cmu.edu /~seitz/pmotion.html (305 words)

	Periodic windows
		As we move away from the window, in parameter space, the intervals of periodic motion become gradually shorter and more infrequent.
		The remaining periods, 6, 4, 6, 5, 6, correspond to tiny periodic windows, which, in practice, are virtually impossible to observe.
		The existence of a universal sequence of stable periodic orbits in dynamical systems which exhibit a transition to chaos via a cascade of period-doubling bifurcations is another indication that chaos is a universal phenomenon.
	farside.ph.utexas.edu /teaching/329/lectures/node58.html (801 words)

	Notes Section 10 (Site not responding. Last check: 2007-10-12)
		For a periodically driven 2nd order nonlinear oscillator a Poincaré map can be obtained by stroboscopically observing the position and velocity at a particular phase of the forcing function.
		Example: the coupled motion of two undamped oscillators may be imagined to take place on the surface of a torus; with circular motion around the small radius representing the motion of one oscillator and motion around the large radius representing the other oscillator.
		If the motion is quasi-periodic, the orbit will (eventually) come close to all points on the surface of the torus.
	www.sun.rhbnc.ac.uk /~uhap045/316/sect10/sect10.html (1185 words)

	Analytic solution
		The final term represents the time-asymptotic motion of the pendulum, and is manifestly independent of the initial conditions.
		It is often convenient to visualize the motion of a dynamical system as an orbit, or trajectory, in phase-space, which is defined as the space of all of the dynamical variables required to specify the instantaneous state of the system.
		Of course, the attractor is termed ``periodic'' because it corresponds to motion which is periodic in time.
	farside.ph.utexas.edu /teaching/329/lectures/node48.html (803 words)

	Lesson 11: Simple Harmonic Motion
		Periodic motion may occur when a particle or body is confined to a limited region of space by the forces acting on it and does not have sufficient energy to escape.
		In this lesson you will study the special kind of periodic motion that results when the net force acting on a particle, often called the restoring force, is directly proportional to the particle's displacement from its equilibrium position; this is known as simple harmonic motion.
		In the figure above, the period of the motion is the time required for one complete vibration.
	www.physics.csbsju.edu /RPEG/no_paper/handouts/Lesson.11.html (2775 words)

	MOTION IN TWO DIMENSIONS and PERIODIC MOTION
		Projetile Motion applet These two types of problems can also be solved graphically using parametric equations on the graphing calculator.
		You can use your graphing calculator to determine how the magnitude of the centripetal force varies the speed with which the object is swung in the horizontal circle, the mass of the object, or the radius of the horizontal circle.
		Kepler's Third Law: The ratio of the squares of the periods (the time needed for one revolution about the sun) of any two planets revolving about the sun is equal to the ratio of the cubes of their mean distances from the sun.
	www.pschweigerphysics.com /2dimmot.html (4171 words)

	Robotics Institute: Affine Invariant Detection of Periodic Motion
		These approaches rely on the assumption that a periodic motion projects to a set of periodic image curves, an assumption that is invalid in general.
		Using affine-invariance, we derive necessary and sufficient conditions for an image sequence to be the projection of a periodic motion.
		Seitz and C.R. Dyer, "Affine Invariant Detection of Periodic Motion," Proc.
	www.ri.cmu.edu /pubs/pub_2851.html (248 words)

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