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Very little material exists for utilizing the computer in the physics classroom, and even that little is not widely known. It is hoped that this monograph will provide some stimulus both to innovation and to discussion of the role of the computer in physics education. The paper describes how this might be achieved with a detailed account of one week of instruction in the physics of the harmonic oscillator, without calculus, for either physics or non-physics majors. The course is organized into three lectures, Days One to Three, and a Laboratory Session. Day One develops the basic first-order numerical integration scheme for computing velocity and position from a knowledge of acceleration and initial conditions. Day Two discusses the nature and languages of computers, and the construction of algorithms for computation, and Day Three is available in four different versions, one for each of the well-known computer languages-- BASIC, FORTRAN, JOSS, and PL-1. A Student Manual and a Teacher's Guide are included in this paper. (GO)

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1. The following paper deals with the oscillatory energy taken up by a simple resonator under the action of white light, and the translatory energy imparted to a molecule by radiation. The first problem has already been treated by Planck: it is solved here in a very simple manner, and the method used, when applied to the second problem, leads to the important result, that a molecule at rest within an enclosure of uniform temperature will, under the action of the radiations, be set in motion with an acceleration that will increase its speed until the average energy reaches a definite value. If the Rayleigh-Jeans laws of radiation be assumed to hold, the ultimate average energy due to radiation alone is two-thirds of that derived from the kinetic theory of gases.

This paper shows a fundamental investigation concerning a non-uniform theory of wave resistance.The author applied to the theory the new method that he analysed in his other paper1) in the conception of acceleration potential. In this paper the author analysed a non-uniform fluid field. of surface wave that is caused by a ship moving with constant velocity describing harmonic oscillations and treated only two dimensional case, but it will be also developed in three dimensional case by the same process.The subject of this paper is a deduction of a velocity potential and an integral equation that determines a relation between motion of a ship and fluid pressure on the ship.

This paper deals with the theoretical study of the pressure rise built up in the liquid trapped between the gears at the meshing point of a gear pump, taking both the local and the convective acceleration of the trapping flow into consideration, the latter of which has been ignored in the author's former paper. The main results are as follows : (1) The convective acceleration has the effect of raising the pressure rise, while the local acceleration has the effect of reducing it. (2) Both effects are comparable and neither of them may be ignored compared with the effect of viscosity. (3) As for the effect only of local acceleration, the present result shows the same tendency and order of magnitude as the former one.

When two parallel cylindrical tanks are connected by a pipe joining the tank bottoms, the liquid can oscillate back and forth between tanks, just as in a U shaped tube. This paper deals with the axisymmetric sloshing oscillations excited in each tank because of the flow back and forth between the tanks. By applying the results from a recent paper [P. G. Bhuta and G. C. K. Yeh, “Liquid Sloshing Due to a Time Dependent Discontinuous Boundary,” Intern. J. Mech. Sci. 7, 475–488 (1965)], the expressions of velocity, pressure, and waveheight are obtained in terms of the liquid density, tank dimensions, pipe radius, and U‐tube natural frequency, which, in turn, is a function of the tank dimensions, pipe dimensions, and the magnitude of acceleration vector. Resonance will occur whenever the U‐tube natural frequency is equal to any one value of the natural frequencies for the axisymmetric sloshing modes of the liquid in each cylindrical tank. Pertinent dimensions to be avoided are pointed out. Extension of the results to asymmetric sloshing based on a paper by Yeh [“Liquid Sloshing in a Moving Tank with a Time Dependent Discontinuous Boundary,” TRW Space Technol. Labs. Rept. EM 14‐12 (6438‐6002 RU‐000) (June 1964)] is also indicated.

The author has already showed in his other paper that the conception of Prandtl's acceleration potential gave a suitable instrument for the analysis of the wave-system generated by a travelling disturbance.In this paper he develops the theory in the three dimensional fluid field of wave-system. The wave-system in three dimensions has been sufficiently investigated by many researchers, but the author synthetically analyses it from a different point of view.

This paper presents an extension of an approach which was previously developed by the author [J. Acoust. Soc. Amer. 49, 629–638 (1971)] to investigate the pressures at spatial points in the field resulting from a specified pulsed velocity notion of a baffled piston. In the present paper an investigation of the farfield pressures radiated from baffled pistons and the characteristics of the time‐dependent energy beam pattern are presented. The earlier approach is shown to reduce to simple expressions relating the time history of the farfield pressures to the time history of the piston motion. It is noted that the pressure at points in the field resulting from a pulsed velocity can consist of a multipulse structure. In different regions of the field, the pulses can be proportional to the piston displacement, velocity, or acceleration. As a result it is shown the pressure pulses may have nonzero average values for a pulsed sinusoidal velocity. For nonsinusoidal pressure fields the energy pattern of an array is defined and expressions are developed for the energy pattern in both the frequency and time domain. Numerical results are presented comparing the beam and energy pattern of a pulsed array. Several generalizations are noted.

The clocks and pendulums used in these experiments are the property of the Royal Society, and were prepared by their direction, under the superintendance of Captain Kater, whose description of them is quoted by the author at the commencement of this paper. The experiments were made during two voyages of discovery in search of a North-west Passage, the first in 1818, and the second in 1819 and 1820; and Captain Sabine details in succession the proceedings at each station, where an opportunity was afforded of landing and setting up the clocks; and concludes by recapitulating the number of vibrations made by each pendulum in the different latitudes in which it was tried, and by stating the deductions regarding the figure of the earth which follow from the acceleration thus determined. In the first voyage, the number of vibrations was ascertained at two stations only; namely, at Gardie House on the Island of Brassa, and on Waygat, or Hare Island, on the West coast of Greenland; the latitude of the first being 60° 9' 42" N., and of the second 70° 26' 17" N. The number of vibrations in a mean solar day at London being 86497·4, at Brassa they were 86530·507, and at Hare Island 86562·6386; giving an acceleration of 33·107 vibrations between London and Brassa, and of 32·1316 between Brassa and Hare Island; or 65·2386 between London and Hare Island.

Importance of the “phase bunching” of resonant electrons in the whistler mode (WM) wave-particle interactions was pointed out by Brice. In this paper, we call attention on the point that there are two different types of phase bunching with two physically distinct phasing mechanisms in the case of the WM wave-particle interaction. One is a longitudinal phase bunching (the Brice type) which is caused by a longitudinal acceleration, while the other is a transverse phase bunching which is caused by a transverse acceleration. The both types are considered separately and examined mathematically and physically. In order to visualize the different characteristics of the two, numerical results on the phasing patterns and the resultant resonant current are shown by computing the nonlinear motion of electrons in a monochromatic WM wave with various initial velocities (36 different initial phase angles ×15 different speed |υ|).

In this paper we consider a mixture of chemically reacting materials with memory. After stating the constitutive assumptions we adopt the usual postulate of fading memory and determine the restrictions which the Second Law of Thermodynamics places on the response functions. Subsequently, we examine the behavior of acceleration waves propagating in such a mixture which is initially in a state of thermochemical equilibrium. We also distinguish between the cases when the equilibrium state is weak or strong, and determine their effects on the wave behavior.

In this paper, the speeds of propagation of acceleration waves in a two‐constituent mixture are developed. The mixture is assumed to behave elastically, and no reaction is assumed to take place. The amplitude of the waves does not have to be small.

When an electron is given an accelerated motion along a straight line, a spherical pulse of electric and magnetic force is sent out, and the maximum force lies in a plane at right angles to the direction of acceleration. The want of symmetry in the distribution of the force with respect to the direction of acceleration of the electron gave rise to the term polarisation. Barkla has shown that the primary X-rays from an X-ray tube are partially polarised, that is to say, that the maximum radiation proceeds in a plane at right angles to the direction of propagation of the cathode rays. If the secondary X-rays are produced by electrons set in motion by the primary pulses we should expect that, under certain conditions, the secondary rays would also be polarised. This has also been shown to be the case by Barkla. Since there is a considerable body of evidence to show that X-rays and γ -rays are similar in kind, it was thought by the writer that it would be of importance to make some experiments in order to discover whether secondary γ -rays are polarised.

In this paper we consider the design of a cyclotron with a magnetic field which travels in the radial direction; a machine of this kind had been proposed by the author. By means of circular windings which are fed by ac generators it is possible to produce one or more concentrated magnetic fields which travel in the radial direction in the gap. Two versions are proposed. In the first, the traveling wave is the field in-which the particles are accelerated. In the second, the traveling wave is superimposed on the usual fixed magnetic field and acceleration takes place by virtue of the combined fields. The spatial distribution of the field in the wave makes it possible to obtain a stability region(1 > n > 0) which is displaced in the radial direction with the radial velocity of the particles. A stability region is also obtained in the case in which the absolute value of the magnetic field of the acceleration region increases in the radial direction. In principle, the system proposed here makes it possible to build cyclotrons with energies as high as desired. In spite of the cyclic-action characteristics of the acceleration, because of the improved focusing, there is reason to believe that the mean intensity can be larger than that which is obtained in the fm cyclotron. Typical calculations are given for accelerators of various energies. These calculations indicate that the weight and size of these accelerators may be much smaller than other accelerators of the same energy.

In this paper, turbulent heat and momentum transfer for a fluid forced through a vertical tube is considered. First, the authors study a shearing-stress distribution in a tube, by taking the buoyancy force and also the inertia force due to acceleration into consideration. It is proved that the effects of both forces operate quite similarly and result in a very rapid decrease of the shearing stress near the wall. By considering how the velocity profile depends upon the shearing-stress gradient at the wall, the authors deduce the criteria for the prominent effects of buoyancy and acceleration. Second, by assuming that the turbulent boundary layer is constructed by the superposition of the locally developed layers, the authors propose an approximate theory to calculate velocity and temperature profiles under the large effects of buoyancy and acceleration. Thirdly, based on the above theory, a criterion of the reverse transition from turbulent to laminar flow is proposed.

Inertial navigation systems usually use gyroscopes to sense angular motion and use accelerometers to sense linear acceleration. It is feasible, however, using only linear accelerometers as sensors, to determine both the angular velocity and the linear acceleration of a vehicle. This paper presents and compares five configurations of linear accelerometers which may be used to determine both the angular motion and the linear motion of a vehicle.

The effect of rocket acceleration on the internal nozzle flow is investigated further by taking into account the effects of total mass variation. This leads to a time-dependant problem which is solved numericaly with the aid of the quasi-static formulas found in the first paper and based on a constant acceleration. These formulae are assumed to be valid for short time intervals. Acceleration effects could be noticeable during the final period of combustion., Hirsch Charles, Jaumotte André Louis. L'écoulement dans une tuyère de fusée accélérée (2e note). In: Bulletin de la Classe des sciences, tome 57, 1971. pp. 1212-1223.

If a rotating machine has its operating speed above its critical one, it must pass the critical speed when accelerated to operating speed or retarted to a halt. This paper deals with the building up of a vibration of uniformly accelerated or retarded the unbalanced rotor which has linear stiffness and damping. The method of contour integral, by which F. M. Lewis worked analogous problem, is used. The figure shows the maximum amplitude concerning to the damping and acceleration. The experimental formula deduced from the calculated graphs is as follows : Remax=3·78√q e-1·16a, a=q0·379γ0·7, 10

An elastically supported, tuned gyroscope is a complex device, but experience has shown that it can be represented by mathematical models by means of which practically all of its characteristic errors can be analyzed and predicted with good accuracy. The gyro angular transfer function, derived in [1], serves as an excellent basis of evaluation of errors due to asymmetries of the gimballing system and effects of rotor angular offsets. The gyro translational transfer function, derived in this paper, may be used in the analysis of errors caused by linear acceleration inputs.

The present paper provides a partial analysis of zero signals in the Sperry tuning fork Gyrotron, as produced by mass unbalance in the tuning fork, unbalance in the tuning fork drive, and asymmetry in the supports. The zero signal is shown to he highly independent of gravity and acceleration.

A simple graphical method for integrating the equation of motion of a particle in any field of force is used as a short laboratory exercise in an introductory course in mechanics. No knowledge of calculus nor differential equations is required of the student. Based directly on the vector definitions of average velocity and acceleration, and on central differences, it is capable of reasonable precision with relatively large steps. Using the three numbers, 6560cm3 = r2a(2τ)2, 53.7 cm = x1 = x−1, and 4.5 cm = y1 = −y−1, the student can develop half an elliptical orbit in 10 steps to about 6% accuracy on a 56 by 86-cm paper sheet in about one hour, and he can see for himself the step-by-step progress of a particle in an inverse-square field. The considerations leading to these or similar numbers are discussed briefly.

This paper deals with the inclusion of in span conditions, such as time‐dependent displacements, in normal‐mode solutions for the dynamic response of structural members. Both displacement and acceleration normal‐mode approaches are discussed.

In obtaining high velocities (10–100 km/sec) by methods employing the mechanical motion of compressible media it is customary to use the flow scheme obtained with shaped charges [1–4]. This paper presents the results of a study of an apparatus that can be used to obtain gas jets in the same velocity range but at higher densities by means of a different type of flow.

From the spectral intensity distribution of solar X-radiation one can conclude that there is a non-thermal contribution, which is effective during the initial phase of a flare. It is reasonable to suppose that the electrons producing the non-thermal radiation have a non-isotropic velocity distribution. Indeed, one should assume that the electrons, during their acceleration, obtain a preferred direction and that only afterwards does their velocity distribution become Maxwellian by means of collisions. Hence the short-wavelength continuous X-radiation in the initial phase of a flare, consisting mainly of bremsstrahlung, should be polarized and should have a non-isotropic angular distribution.In papers presented to the IAU-Symposia in Budapest 1967 (Elwert, 1968) and in Leningrad last May, the polarization of X-radiation from electrons of a few keV accelerated in solar flares has been calculated using energy distributions based on the observations of Pounds et al. obtained with the satellites Ariel I and OSO-4.

The problem of nonstationary acceleration of a conducting gas in a channel is solved, together with the problem of a discharge in an electric-circuit. As distinct from other papers, in which the typical solution assumed a thin cluster subject to acceleration, we examine the case in which the gas flow fills the entire channel. The motion of the gas in the channel is examined in one-dimensional formulation, under the assumption that the particle transit time in the channel is small compared to the discharge time and that the electromagnetic force is large compared to the pressure gradient.

This paper gives a short description of some of the properties of accelerators having a vertically increasing field. A discussion is given of the requirements which must be met for optimum acceleration, as well as questions dealing with the existence of equilibrium orbits, the stability of betatron oscillations and the particle acceleration process in accelerators of this type.

This paper is devoted to an application of the theory of the transition stage (the process of transition from betatron to synchrotron acceleration) to the FIAN 250 Mev synchrotron for the case when the accelerating field is established adiabatically. From the experiments and calculations that have been carried out it is possible to judge the correctness of the theory as applied to accelerators of this type. Some characteristics of the electron beam during the betatron stage, for example, the electron energy distribution, have been obtained from the experimental data.

In this paper it is shown that the capture time in a synchrocyclotron depends critically on the starting phase. The total capture time oer acceleration cycle has been derived from an integration over the starting phase interval 0°−60°. The fact that the phase oscillations are damped with increasing energy has been used to minimize the acceleration time. Intensities are estimated by means of the presented results on capture efficiencies and from available space-charge theories. A synchro-cyclotron of 600 MeV energy could be improved to deliver at least 60 μA of protons.

with the case for arbitrary loss usually presented. The TWR equations are shown to take the identical form, in the absence of a mismatch, as the expressions for the standing wave superconducting accelerator with beam loading. 6 At SLAC a twefoot long TWR test accelerator (project Leapfrog) is currently under construction. A thorough understanding of TWR behavior is necessary for the successful design and operation of such a device. In the following sections of this paper the basic relations describing the behavior of the TWR accelerator are summarized. In the final section some implications of the theory for the Leapfrog accelerator are given. The description of TWR behavior as presented here is necessarily brief. Details of the derivations and a more extensive discussion are given in Ref. 7.

In a missile flying a proportional navigation course, the missile heading rate is made proportional to the indicated line of sight rate. While for stationary targets the resulting differential equations of motion can be readily integrated, this is no longer the case for moving targets. To obtain closed-form expressions convenient for the evaluation of trajectory parameters, the assumption is made in this paper that for moving targets, the angular rate of the closing velocity vector is made proportional to the line of sight rather than the actual heading rate.

Pitch angle distributions (PAD) of energetic electrons relate to a wide variety of magnetospheric processes. Wave-particle interactions (turbulence, instabilities) act on a time scale comparable to the particle gyro period; betatron acceleration is important on time scales of the bounce period to minutes; and drift-shell effects are important on time scales of the azimuthal drift period. A study of pitch angle effects can provide important information on the static and dynamic aspects of field topology. Our interest in this paper is primarily with the drift shell effects.

IT is a little surprising to find in Dr. Shaw's paper (December 16, 1913), “. . . He (Mr. Whipple) points out that we have no special name for the unit of acceleration.” In NATURE of June 25, 1914, Mr. Whipple proposed the name leo. So long ago as 1909 Wiechert used the term “gal” in the report for the Gottingen earthquake station for that unit, being the first syllable of Galileo, whence Mr. Whipple derives his “leo.” Others, as well as myself, have used “gal,” or rather “milligal,” in analyses of earthquakes. A milligal is approximately a millionth of g. Dyne is the unit of force, gal the unit of acceleration.

In a paper contributed to the Philosophical Magazine in January last, I expressed an opinion that Chastaing’s idea regarding an acceleration of oxidation being caused by red light might prove true in regard to the oxidation of the photographic image, and elsewhere that Becquerel’s coloured spectra and Draper’s reversed spectra might be explained on the same principles. Owing to want of time until this last week, I have been unable to investigate the matter, but can now affirm that such is the case as regards oxidation of the photographic image. Silver bromide, free from contamination, emulsified in collodion, which had been previously carefully purified, was spread on a plate, and exposed to diffused light. It was then submitted to the action of the solar spectrum, while immersed in a solution of potassium permanganate, or hydroxyl. When the strength of the permanganate, or hydroxyl, was correct a reversed image of the least refrangible end of the spectrum was obtained, an increase in oxidation taking place when the red rays acted, the reversal taking place somewhere near D, extending into the ultra-red.

The sonic block concept has proven to be an extremely effective method of reducing compressor radiated noise. This type of silencer is based upon the classical fact that when a fluid is traveling in a direction opposite to and at a speed equal or greater than the velocity of propagation of a disturbance in that fluid, then the disturbance cannot be transmitted upstream through the fluid. Since the principle of operation involves only direction and relative speeds, its acoustical performance is independent of frequency. The amount of noise reduction is limited only by (1) suppressor wall noise radiation; (2) noise escape through boundary layer at the sonic block; and (3) fluid acceleration noise. This paper describes sonic block designs for turbojet engine axial compressors and small industrial screw type units. Actual noise reductions are presented for a 225 lb/sec axial flow compressor and a 2 lb/sec Lysholm type unit. In the case of the high speed axial flow unit, high frequency blade noise was submerge...

Most high intensity acoustic sources are in motion relative to the undisturbed atmosphere. This paper presents improved methods for calculating the sound generated by sources in arbitrary motion. A number of examples are presented, the principal current applications being to problems of forces on a rotating system such as on a fan or helicopter. General expressions for simple sources, forces, and acoustic stresses in motion are given. It is found that the effects of acceleration is to cause additional, higher‐order terms in the radiated sound field. A derivation of the basic results was given earlier [Proc. Roy. Soc. (London) A286, 559–582 (1965)].

This paper describes three accelerometer calibrators. These calibrators were developed to provide a convenient means for calibrating lightweight accelerometers of the types used for measuring accelerations on airplanes in flight. The first calibrator is a shaking table having a sinusoidal motion with frequencies of 20 to 110 cycles per second and accelerations up to 80 gravity; the second is a portable calibrator producing a known pulse of acceleration with a peak value between 1 and 20 gravity; and the third is a centrifuge, which develops a maximum steady acceleration of about 1,000 gravity.