影响单摆振动周期的参数研究

应用振动分析的方法,研究了单摆的周期受摆角、摆球的线度、地球纬度、摆球离地面的高度、介质黏度和介质密度参数的影响;作出了周期比随参数变化的曲线.结果表明:单摆的周期随摆角、摆球的线度、摆球离地面的高度、介质黏度和介质密度的增大而增大,随地球纬度的增大而减小.     

单摆实验的数值理论分析

采用理论数值分析的方法对单摆进行研究,结果发现单摆由小角到大角的摆动过程中振动图像在由线性(小角)到非线性(大角)缓慢变化,角度越大非线性现象越明显;基于第一类完全椭圆积分和数值积分的方法计算周期,结果证明周期与摆长、角振幅相关;不同摆长的周期分析结论是摆长较小时有利于实际实验测量,其带来的相对误差较摆长较大时更小.为实际操作方便角振幅(摆角)可适当增加,对实验结果不会引入较大误差.     

单摆周期公式的来源和推导

本文介绍了单摆周期公式发现的历史,并提供了一种较简单的、接近惠更斯时代知识背景的推导方法. 一 问题的缘起 我们在上《单摆》这一节课,讲到《单摆振动的周期》这部分时,一般用实验演示单摆振动的周期与振幅、摆长、摆球的质量、重力加速度的关系.     

基于MATLAB下对单摆实验中大摆角问题的讨论

借助MATLAB计算软件,研究无阻尼状态下单摆的大摆角运动,给出了任意摆角下单摆运动周期的精确解。同时利用MATLAB函数库中的ode45函数,求解出大摆角下的单摆的运动方程及其运动规律,为单摆实验中大摆角问题的讲解提供了较好的教学辅助手段。     

用单摆测重力加速度的改进

1 实验概况 由单摆振动周期公式可得,所在地重力加速度由公式 实验中单摆不可能完全符合单摆模型的要求.为了减小各种不符合因素对单摆周期的影响,常规的学生实验总要求轻质细绳的长度超过1m.球形重物(摆球)直径小于1cm,摆角小于5°.     

摆角对单摆周期的影响

1引言利用单摆周期公式T=2π测量重力加速度的实验中,要求摆角小于5°以减小误差．但是摆角的大小对单摆周期到底有什么影响?下面用能量守恒的方法来研究在保守力的作用下自由单摆(忽略阻力)的周期．     

单摆周期的测量误差与最大摆角的关系

对于单摆的周期,用周期公式算出的理论值T_0与实验测定值T之间的误差,随摆角增大而增大,最大摆角一般应小于5°.为了全面了解单摆周期误差随摆角增大而增大的情况,必须深入探讨周期与最大摆角的关系.     

用数字计时器测定单摆周期

单摆在摆角很小的情况下,振动周期为:T=2π(g/l)~(1/2)(1)测得单摆的振动周期T及摆长l,就可算出重力加速度g值,即:g=4π~2l/T~2(2) 通常,单摆的振动周期是用停表来测定。由于停表精度不够,特别是单摆振动周期的起讫位置不易判断,以致按停表的时刻提早或推迟,周期不易测准。如采用能测三次挡光时间     

如何实现宏观量子单摆

利用等效质心方法描写单摆运动,经典力学通过牛顿方程得到摆球在空间做周期振动,而量子力学却给出完全不同的结论:摆球做无"周期"的随机运动.本文分析了量子力学等效质心模型成立的条件,在此基础上计算了经典单摆过渡至量子单摆的实验条件,表明在目前的实验水平上观察宏观摆球(微米量级)的空间量子跃迁行为是简便易行的.     

椭圆曲面摆参数振动的数值计算及仿真

为研究变摆长参数振动的规律,以椭圆曲面摆装置为对象,根据刚体定轴转动定律及椭圆曲线方程,构建了椭圆曲面摆的二阶变系数齐次微分动力学方程.运用四阶龙格-库达法对方程进行数值求解,并结合MATLAB软件绘制了椭圆曲面摆振动不同的图像,给出椭圆曲面摆在无阻尼状态时的方程通解形式,在此基础上,讨论了不同参数对椭圆曲面摆振动特性的影响情况.研究表明,椭圆曲面摆与单摆振动类似,在无阻尼状态时小球摆动符合正弦函数变化规律,小球摆动周期受到阻尼系数、椭圆曲面几何尺寸、振幅等参数影响.研究结论丰富了关于变摆长单摆参数振动教学内容.     

Point defects on graphene on metals

Understanding the coupling of graphene with its local environment is critical to be able to integrate it in tomorrow's electronic devices. Here we show how the presence of a metallic substrate affects the properties of an atomically tailored graphene layer. We have deliberately introduced single carbon vacancies on a graphene monolayer grown on a Pt(111) surface and investigated its impact in the electronic, structural, and magnetic properties of the graphene layer. Our low temperature scanning tunneling microscopy studies, complemented by density functional theory, show the existence of a broad electronic resonance above the Fermi energy associated with the vacancies. Vacancy sites become reactive leading to an increase of the coupling between the graphene layer and the metal substrate at these points; this gives rise to a rapid decay of the localized state and the quenching of the magnetic moment associated with carbon vacancies in freestanding graphene layers.     

基于Matlab分析负荷对多联机IPLV的影响

多联机有其特殊的优点,但是不同部分负荷的组合对IPLV的影响仍需进一步研究。文中建立IPLV与部分负荷的相关公式,运用MATLAB软件分析不同卸载级负荷与IPLV的关系,从而确定不同部分负荷的最优组合。     

Remarks on KdV-type flows on star-shaped curves

We study the relation between the centro-affine geometry of star-shaped planar curves and the projective geometry of parametrized maps into RP¹. We show that projectivization induces a map between differential invariants and a bi-Poisson map between Hamiltonian structures. We also show that a Hamiltonian evolution equation for closed star-shaped planar curves, discovered by Pinkall, has the Schwarzian KdV equation as its projectivization. (For both flows, the curvature evolves by the KdV equation.) Using algebro-geometric methods and the relation of group-based moving frames to AKNS-type representations, we construct examples of closed solutions of Pinkall’s flow associated with periodic finite-gap KdV potentials.     

X-ray diffraction on chlorine adsorbed on graphite

Cl₂ layers adsorbed on Grafoil have been investigated by X-ray diffraction between 78 and 285 K. Mono- and submonolayers crystallize in a parallelogram lauttce, incommensurate with the (001) graphite surfaces, the molecules oriented almost perpendicular to the surface. The structure is closely related to that of the (001) planes of three-dimensional solid chlorine. For coverages above the monolayer completion bulk crystalization sets in.     

Note on duality on polarized symplectic manifolds

In this note we use some of the results of [3] to derive a general duality theorem for the cohomologies of foliated structures on a manifold. The result is applied to the special case of a symplectic manifold M on which the foliation is given by a complex polarization F in the sense of geometric quantization. We obtain, for example, a rigorous proof of the fact that for a smooth function ƒ on M whose Hamiltonian vector field leaves F invariant, the spectrum of the corresponding prequantization operator v(ƒ) coincides with the spectrum of its transpose, under the above duality. This latter result was obtained by Simms in [12] under certain hypotheses. Proofs of the validity of those hypotheses are now available in the literature; cf. [3] and [7].     

Space-charge effects on multipactor on a dielectric

Analyzes the effects of space charge shielding on the steady state of a multipactor discharge on a dielectric. Analytic methods are used to obtain an exact function for the potential in the discharge, assuming a Maxwellian distribution of emitted electrons. An equation for the amount of power deposited on the dielectric by the multipactoring electrons, for a given saturation level, is given. A simple method for obtaining the saturation level, for a given material, is obtained