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In a previous paper  certain characteristics of the behavior of an elastic string undergoing periodic vibrations of moderately large amplitude were established. In this note, the same basic result is obtained in a manner which is mathematically more satisfactory. Furthermore, a refinement of the solution associated with the periodic motion of lowest frequency is obtained. It is convenient to postulate a material which obeys the stress-strain law Here, T0 is the rest tension, A the restdoi:10.1090/qam/28511 fatcat:p43o7h7sqjfsdkdqqbpen6puse