半无界弦自由振动问题延拓的修正

The correction of semi-infinite string free vibration solutions continuation

视半无界弦为无界弦x>0的部分,半无界弦的自由振动问题可以通过适当延拓,用达朗贝尔公式求解.对应于第一类、第二类齐次边界条件的半无界弦自由振动问题的延拓应该具有更一般的形式,而不是只能采用奇延拓或偶廷拓.定解问题的衔接条件要求延拓具有连续性.

Looking semin-infinite string as the x>0 part of infinite string, through some fitcontinuation, the free vibration problems can be work out by d'Alembert formula. When the boundarycondition is the first or the second homogeneous boundary condition, there should be morecontinuations, not just be odd or even continuation as we now know. The definite solutions connective condition asks for the continuation continuity.