关于玻尔共振实验中几个问题的理论探讨

Theoretical discussion on several problems about the Bohr resonance experiment

在建立空气媒质中阻尼运动方程的基础上,定义了在能量耗散情况下的品质因数,以及没有强迫力的欠阻尼条件下稳定方程之解;推导出了系统在t时刻所储存的机械能公式,进而得出品质因数与相关参量的关系;根据系统达到稳定且振幅与系统产生共振时的最大振幅,推导出了半宽带关系式;通过建立强迫力功率(P1)与阻力做功功率(P2)表达式,并取t到(t+T)为积分上下限求解平均功率,获得二者大小相等符号相反,即P1+P2=0,得出强迫力做功正好是系统补充的能量.这些问题的讨论,为同行和学生起到了抛砖引玉作用.

Based on the damped motion of air medium equation, the quality factor of energy dissipation is de- fined, the solution of stable equation is obtained without the forcing underdamped condition. The mechanical energy formula of system stored in the time t is derived, and the relationship between the quality factor and the related parameters is got. According to the maximum amplitude of the system reaching steady amplitude and the system resonance, the half broadband relationship is deduced. Through the establishment of forcing power （P1） and resistance （P2） expression formula, the conclusion two equal size minus opposite, namely, P1 ＋P2 =0, are obtained, with t to （t＋T） for solving the integral upper limit and lower limit of average power, and the result are got that force work is equal to the system to add energy. The discussion of these issues can play guiding role for colleagues and students.