북의 진동모드에 대한 이론적 고찰

Abstract

The vibration mode characteristics of a drum were analyzed using the Green's function method. In our experimental system, the drum was percussed by external vibrator at polar position (r', θ' ). The normal modes appeared on the drum in case of k=k_(mn), and they were changed by the position of driving force (r', θ'). The maximum amplitude of the mode was also formed along the angle θ'. When the radius of driving position r' was changed, the amplitude of the mode was proportional to the value of Bessel function(J_(m)(kr')). Therefore, the maximum amplitude appears where the value of J_(m)(kr') is maximum. If k≠k_(mn), the drum had abnormal modes with less amplitude than those of the normal modes. In this case, the shapes of these abnormal modes those became to be irregular with the position r'. However, we observed, that the amplitude of the modes was not changed by the position of driving force r'. In conclusion, we propose that the systems explored in our studies can be utilized to describe the concepts of probability density and mode of wave formation in Quantum mechanics.