大摆角单摆“周期”变化的解析解及其实验应用

大摆角单摆实验由于忽略空气阻尼带来周期测量的系统误差.基于弱阻尼大摆角单摆的运动方程,推导了累计"周期"随摆次变化的解析公式,分析了"周期"随摆次减小的基本规律.结合实验数据分析,验证了将其用于大摆角单摆实验进行系统误差修正,从而通过累计测量减小随机误差的可行性.     

单摆非线性特征的研究

通过实验精准地测量了大摆角情况下单摆的摆角与周期,同时利用Matlab软件,求解了非线性的单摆动力学方程.理论模拟与实验测量的结果进行对比分析,证明了大摆角单摆具有典型的非线性特征.     

基于视频图像处理的单摆振动特性研究

针对目前单摆振动特性研究方法的不足,基于视频图像处理技术,提出了一种实验测量与数值计算相结合的方法来研究单摆的振动特性。该方法能计算出单摆摆长、位移、周期和最大摆角。绘制了单摆在几种任意摆角运动下的位移时间曲线,分析讨论了单摆周期随摆角的变化规律。与传统研究方法相比,该方法简单直观且计算精度高。     

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.     

巧用智能手机拓展单摆实验

将智能手机运用在"非常规"条件下的单摆实验中,利用手机中的光线传感器,分别设计了单摆阻尼运动实验和测小摆长、大摆角时的重力加速度实验,拓展了常规单摆实验的内容.     

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。     

均匀磁场中磁性液体的磁表面张力系数实验研究

基于特殊性能的磁性液体增设了综合性设计性实验项目,根据项目式教学法初步实现了以学生自我训练为主的教学模式.本文设计了磁性液体磁表面张力系数智能测试仪,研究了均匀磁场中4种不同类型磁性液体的磁表面张力系数随磁感应强度的变化规律.随外加磁场磁感应强度的增强,磁性液体的磁表面张力系数增大,主要是磁场增强了磁性颗粒之间的相互作用力.磁感应强度相同时,载液质量对磁性液体的磁表面张力系数影响较大,载液质量越小,单位体积内融入的磁性颗粒数量越多,导致磁性液体的磁表面张力系数越大.表面活性剂种类对磁性液体磁表面张力系数的影响也较大,由于油酸对磁性颗粒的吸附作用比PBSI-941表面活性剂强,油酸官能团较早吸附在磁性颗粒表面,限制了磁性颗粒进一步长大,导致MFO-4磁性液体磁表面张力系数较小.     

基于不确定度理论的大摆角单摆平均“周期”测量的最佳累计次数研究

由于空气阻尼的作用,测量大摆角单摆“周期”时,测量累计次数增加造成平均“周期”不断减小,在无阻尼实验设定下,系统误差随之增大而随机误差却因此减小.基于弱阻尼大摆角单摆的运动方程与“周期”计算公式,通过数值计算不同摆长与摆角下使不确定度最小的最佳累计摆动次数,发现如果进行单次测量,采用秒表测量时最佳累计摆动次数往往需要大于20次,采用光电门测量时,在不同的摆长和摆角下,测量次数往往也不止1次;而如果采用多次测量,则可以显著减小每次测量所需要的最佳累计摆动次数.采用计算所得最佳摆动次数测量可以将周期测量的不确定度减小到A类不确定度的√2倍.     

用智能手机对载流导体三维磁场的测量研究

本文利用智能手机中的磁传感器来测量载有电流的导体所激发的三维磁场。测量长直导体与不同半径圆环形导体在三个轴（Bx轴、By轴、Bz轴）方向上的磁感应强度。据实验结果显示，手机测得的磁感应强度在一定范围内与理论值较为一致。根据实验结果研究智能手机中磁传感器在误差允许的范围内对磁感应强度的测量精确度和测量范围，并分析影响精确度的因素。探究手机能否作为测量磁场的工具应用于学生实验室，在一定程度上代替昂贵的实验设备进行磁场测量实验。     

第22届亚洲物理奥林匹克竞赛实验试题1的介绍与解答

第22届亚洲物理奥林匹克竞赛实验试题1为磁学黑盒子(Magnetic black box),试题利用智能手机中的磁力计测量磁感应强度随时间的变化,从而研究磁铁在无磁性空心管中的运动及空心管的材料.本文详细介绍了实验试题1的内容,并给出详细解答.     

智能传感器在大学生物理实验中的应用

实验利用智能传感器测量复摆大角度振幅的周期,同时用计算机控制复摆得到实验数据,再利用配套软件根据数据做出图形;配合Excel对实验图形进行分析处理,得出结论。     

Self-diffusion measurements by a constant-relaxation method in strongly inhomogeneous magnetic fields

The simple pulse sequence thetax-tau1-2thetay-tau1+tau2-2thetay-tau2-Hahn echo used to measure the self-diffusion coefficient D under constant-relaxation condition, i.e., for tau1+tau2=const. was investigated in the presence of strongly inhomogeneous static as well as radiofrequency magnetic fields. The encoding of the Hahn-echo amplitude by the pulse flip angle and diffusion was evaluated by taking into account the spatial distribution of the off-resonance field, the strength and orientation of the local field gradients, and the pulse flip angles by a computer simulation program. As input files, this program uses maps of static and radiofrequency fields, and the D coefficient can be evaluated from the time dependence of the Hahn-echo amplitude. The method was applied to a mobile one-sided NMR sensor, NMR-MOUSE with a bar magnet by measuring D for a series of liquids with different viscosities. The method was shown to be particularly useful for measuring D of solvents in elastomers without the need for measurements of the transverse relaxation rates. The self-diffusion coefficient of toluene in a series of crosslinked natural rubber samples was measured and correlated with the crosslink density. Finally, the method was applied to measure the diffusion anisotropy of free water in bovine Achilles tendon.     

基于LP21模式的光纤弯曲传感器

设计并研制了一种基于LP21模式的新型光纤弯曲传感器。该传感器通过检测敷设于弹性基片上的光纤所传输的LP21模式光斑图像的旋转,实现对弯曲值的高精度测量。运用光纤耦合模理论和弹光效应求解LP21的模方程,证明该模式具有弯曲无关和扭转线性的特性,并检验了光纤弯曲传感器对不同结构参数和环境温度下的性能。实验结果与理论分析相吻合,证实该传感器具有较大的线性动态范围,温度稳定性高,且能辨识弯曲方向。     

激光单摆演示仪的研制与应用

设计的激光单摆演示仪是利用霍尔传感器测量摆球的摆动周期,通过演示仪底盘上的小型激光器可观测摆动面的偏转,将计时、计数、测角等功能合为一体,有效摆动时间内能够分辨出地球的自转现象.     

Surface thermal lens technique with an obliquely-incident probe beam

Surface thermal lens (STL) signal produced by a cw modulated top-hat beam excitation is detected by an obliquely-incident probe beam. The dependence of the STL amplitude on the incident angle θ of the probe beam is experimentally investigated. The STL amplitude as a function of the detection distance is measured at different angles of incidence. The results show that the maximum STL amplitude and the optimum detection distance, where the maximum STL amplitude is obtained, decrease by cosθ as the incident angle increases. These experimental dependences are well explained by a simple theoretical model.     

用微元法推导无阻尼单摆运动任意角度下的周期公式

对单摆运动进行了讨论。通过对单摆进行能量分析,得出了单摆角频率与角度的关系式,然后运用微元法,推导出了单摆的理论周期公式。计算结果表明,所得到的单摆运动周期的理论公式与展开公式符合得很好。     

传感器和Origin7.0软件在电脑控制韦伯福斯摆的实验研究中应用

研究用电脑控制韦伯福斯摆的实验中,用光电传感器、位移传感器和力传感器测量摆的振动周期和摆幅、角速度等及弹簧的劲度系数,由此来学习一种测量刚体转动惯量的方法。     

混沌的解析与e-measure混沌摆实验

阐述了混沌的建模;利用旋转移动传感器对物理摆的相空间轨迹进行了实时测量,记录了混沌产生过程中相空间的角位移和角速度的变化。证实了混沌对初始条件的敏感性,以及混沌中3周期点的存在。     

An autoparametric energy harvester

This paper presents a numerical study of an autoparametric system composed of two elements: a pendulum and an excited nonlinear oscillator. Owing to an inertial coupling between the two elements, different types of motion are possible, from periodic to chaotic. This study examines a linear induction of an energy harvester depending on the pendulum motion. The harvester consists of a cylindrical permanent magnet mounted on a rotor and of four windings fixed to the housing as a stator. When the pendulum is rotating or swinging, the converter is generating energy due to magnetic induction. In this paper, a method utilizing parametrical resonance for harvesting energy from low frequency vibrations is studied. The authors compare energy induced by different types of pendulum motion: swinging, rotation and chaotic dynamics. Additionally, voltage values for different parameters of excitation are estimated.     

Chaos and transient chaos in an experimental nonlinear pendulum

Pendulum is a mechanical device that instigates either technological or scientific studies, being associated with the measure of time, stabilization devices as well as ballistic applications. Nonlinear characteristic of the pendulum attracts a lot of attention being used to describe different phenomena related to oscillations, bifurcation and chaos. The main purpose of this contribution is the analysis of chaos in an experimental nonlinear pendulum. The pendulum consists of a disc with a lumped mass that is connected to a rotary motion sensor. This assembly is driven by a string-spring device that is attached to an electric motor and also provides torsional stiffness to the system. A magnetic device provides an adjustable dissipation of energy. This experimental apparatus is modeled and numerical simulations are carried out. Free and forced vibrations are analyzed showing that numerical results are in close agreement with those obtained from experimental data. This analysis shows that the experimental pendulum has a rich response, presenting periodic response, chaos and transient chaos.