Vibrations of a String with Time-Variable Length

抄録

Free and forced vibrations of a string with time-variable length are treated theoretically under the assumption that the variation rate of the length is small. The solutions are obtained n the form of a power series of a small parameter which prescribes the variation rate of the length. The theoretical analysis shows that the free vibration has a nature of a travelling wave. As to the forced vibration occurring during a transition through the fundamental resonance point, the analysis shows that the amplitude becomes maximum slightly later than the moment when the "natural frequency" of the system coincides with the frequency of the external force. An experimental analysis is performed for the forced vibration. The comparison of the results of the theoretical analysis with those of the experimental analysis shows a fairly good agreement.