单自由度振系固有频率不含弹簧静变形的充要条件

教材示例几乎都使用固有频率表达式不显含弹簧静变形的例子,但确实存在相反的情形.本文针对单自由度振动系统,研究了弹簧静变形从固有频率表达式中消失的充要条件.由于采用了能使广义质量为常数的广义坐标,从而只用研究系统的势能.研究发现静变形消失的充要条件是:在静平衡位置弹簧轴线与其运动端点的轨迹相切,且以弹簧运动端点位移为广义坐标所得到广义质量对广义坐标的导数应为0.     

关于质点弹簧系统在重力作用下的静平衡与振动

质点弹簧系统在重力作用下的静平衡状态由此系统的有效质量决定;其本征振动频率wn则由弹簧与质点的质量之比ml/m2 决定;Wn的平均值w与w2由此系统的初始条件决定,不同的初始条件导致不同的平均值.例如,若u(y,O)=uαf(y)=uaf(y)=u0y,则可得w2=k/(m2+1/3m1).并给出一个计算θ1:w1/w0的近似公式.     

对《质点从可自由移动的凹曲面上滑下速度、加速度和时间》的一点补充

根据质点从可自由移动的凹曲面上滑下的时间表达式,用泛函得出质点另一种下滑轨迹的曲线方程,指出了质点沿此曲线运动时所用时间具有极小值.     

转动弹簧的微变形分析及其应用

教材中经典的弹簧振子的弹簧不会转动,但工程上弹簧轴线会转动的情形比比皆是。弹簧轴线转动会造成几何非线性,但是围绕平衡位置的微幅振动仍是振动学习的最重要任务。本文先用解析法导出了弹簧微变形的近似表达式,再利用直观的几何关系验证这一表达式,而后者易于理解和记忆。利用3个例题对表达式的威力进行了验证。     

物理奥林匹克竞赛实验专题

第 7期试题解答注意 ,这里切不可将重力加速度当成常量 .相反 ,它是一个待测的物理量 .由于地球表面物体 (质量为 m)所受的重力近似等于它与地球之间的引力mg=Gm MR2式中 G为万有引力常量 ,M为地球质量 ,R为所要测定的距离 .显然 ,重力加速度 g不能视为常量 ,而是要通过测量予以确定 .质量为零的弹簧在砝码作用下沿竖直方向作简谐振动的公式为T=2 π mk式中 k为弹簧的劲度系数 .改变砝码质量 ,并测量振动周期 ,通过 T2 -m图的斜率可以求出 k.由胡克定律可得f =mg=kx式中 x为弹簧在砝码作用下的位移 .改变砝码质量并测量相应的位移 ,因 k…     

竖直方向简谐振动中1/2kx~2的物理意义

竖直方向简谐振动中１２ｋｘ２的物理意义范素华王培吉（山东建材学院，济南２５００２２我们知道，若将水平的弹簧振子置于竖直方向，则物体是在弹性力和重力的共同作用下作谐振动，仅仅是振动的平衡位置由原来的弹簧自由伸长位置向下移动了一段距离ｌ０（ｌ０＝ｍｇ／ｋ...     

复合场中的滚轮线

带电质点在正交的匀强电场(重力场)和匀强磁场中运动,轨迹为滚轮线.处理滚轮线问题的关键是构造匀速直线运动以平衡电场力(重力),从而将带电质点的运动分解为匀速直线运动和匀速圆周运动,简化问题的处理过程.     

质点沿可自由移动的光滑凹槽的运动分析

分析了质点在可自由移动的凹槽上运动的运动平面与凹槽的交线是一般曲线的情况,给出了质点在静止参考系中运动的轨迹方程和严格等时振动的条件,求出了质点沿几种常见曲线运动的周期.     

学习“加速度减小的加速运动”的思维障碍及其对策

在高中的物理学习中,我们经常会遇到加速度减小而速度增大的运动,从高空有一小球自由下落,与直立的轻质弹簧发生碰撞,在小球到达平衡位置的过程中,由于小球所受的向下的重力不变,而向上的弹力逐渐增大,但小于重力,所以小球所受的合力方向向下,大小逐渐减小,因此,加速度减小,但运动速度逐渐增大,但许多学生错误地认为加速度减小,速度一定是减小的,在简谐运动中,弹簧振子回到平衡位置的运动过程,弹簧振子做的也是加速度减小的加速运动,再比如,汽车以恒定的功率起动过程中,所做的运动也是加速度减小的加速运动,这类运动相对于匀变速直线运动要复杂,学生学习这部分知识普遍感到困难,如果不能正确的理解和掌握加速度减小的加速运动,将直接影响对运动物体全过程的正确分析,也就无法处理和解决这一类问题,所以把加速度减小的加速运动作为一个专题进行全面而系统的学习,为解决这类问题打下基础是很有必要的.     

非惯性系中单摆周期研究

 高中物理“单摆”的考查重点是单摆周期的计算,其中尤以在匀变速运动系统中的单摆周期的计算为难点。传统方法是求出单摆的等效重力加速度ｇ′,代入周期公式Ｔ=2πｌ/ｇ′即可。而等效重力加速度ｇ′的求法是:先确定单摆在系统中的平衡位置,然后求出平衡位置时摆线对摆球的拉力Ｔ′,最后确定ｇ′,ｇ′=Ｔ′/ｍ,ｍ为摆球质量。上述方法能有效地解决问题,但其物理意义不明显。本文拟从动力学角度出发,在非惯性系中讨论此问题。首先就一般情况,得出一个普遍适用的公式,然后对几种特殊情况加以分析。1.沿倾角对α的斜面匀加速上滑的非惯性系实例:放在沿斜面匀加速上滑的小车中的单摆。     

关于"太阳在银河系中所受引力与到银心距离r的关系"的讨论

讨论了银道面内的引力场强分布和太阳在银河系中所受引力与到银心距离r的关系，指出引力场强g并不是与r的平方成反比，这是由于银河系的大小和形状不能忽略造成的．强调了万有引力定律的适用条件．     

On the predictability of the positions of the convergence zones in the ocean

The disagreement between the experimental and calculated positions of the first convergence zone are known from many publications. The most probable cause for such a disagreement, namely, the incorrect specification of the input data for the calculations, is considered. The lack of simultaneity between the hydrological surveys of the region and the acoustic experiments is emphasized. The experimental data obtained by the author in five ocean regions are presented. These data characterize the diurnal variability of the distance from the source to the nearest boundary of the convergence zone. The relations proposed by different researchers for calculating the sound speed from the temperature, salinity, and hydrostatic pressure are analyzed. It is shown that these relations lead to a substantial difference in the estimated depth dependence of the hydrostatic gradient of the sound speed. The position of the first convergence zone is calculated for the propagation conditions determined by vertical temperature and salinity profiles with the subsequent recalculation of these profiles into sound speed profiles by using eight different formulas known from the literature. It is shown that different formulas lead to different values of the distance to the first zone; this difference is substantially greater than that between the calculations and experiment. The necessity of improving the recalculation relations in view of the experimental data on sound propagation in natural oceanic waveguides, including the data on the actual positions of the convergence zones, is emphasized.     

On the calculation of the bremsstrahlung in the region of the plasma frequency

On the basis of the classical theory of radiation produced in incomplete Coulomb interaction, a formula is derived for the coefficient of the bremsstrahlung of fully ionized plasma. In the region of rectilinear approximation a comparison is made with the results of the quantum formula derived from the Born approximation. Furthermore, the influence of dispersion upon the emission coefficient is taken into account; some relations for the region of dispersion are given.     

Dependence of the Intensity of the Spectral Lines and the Composition of the Sample and the Plasma Parameters of the Unipolar Arc

The investigation was made of the dependence of the intensity of Tl, Ga, Mo, Mg, Mn, Sn, Bi, Ni, Zn, Pt and Au spectral lines and the plasma parameters (temperature T, electron concentration n_e, degree of 6 ionnization α) from concentration of lithium additive.     

Extracting the wavefunction of the LSP at the LHC

We consider associated production of squarks and gluinos with the lightest supersymmetric particle (LSP), or states nearly degenerate in mass with it. Though sub-dominant to pair production of color SU(3)-charged superpartners, these processes are directly sensitive to the wavefunction composition of the lightest neutralinos. Exploiting event-shape variables - including some introduced here for the first time - we are able to identify the composition of the LSP by selecting events involving a single high-pT jet recoiling against missing transverse energy. We illustrate the proposed technique on a set of benchmark cases and propose methods for applying these results in more realistic experimental environments.     

Set the controls for the heart of the Sun

In this paper we describe experiments conducted with high-power lasers that are attempting to replicate, for a very short time and in miniature, conditions found in the Sun. Experiments to date have reached conditions in the outer part of the Sun. To reach the Sun's centre requires compression of material to very much greater than solid density and heating to over ten million degrees. To achieve this, a new class of experiments and a new generation of high-power lasers are required.     

On the Question of the Source of the Apokamp

Technical Physics - The object of this work is the apokamp—a new type of plasma jet, which is formed from a bright offshoot emerging at the bending point of a channel of a high-voltage...