NONSTATIONARY VIBRATIONS OF A STRING WITH TIME-VARYING LENGTH AND A MASS-SPRING SYSTEM ATTACHED AT THE LOWER END

The purpose of this paper is to study the nonstationary vibration of a string with time-varying length and a mass-spring system attached at the lower end. The string is hung vertically and excited sinusoidally by a horizontal displacement at its upper end. The mass is supported b y a guide spring horizontally and has two-degrees-of-freedom, vertical and horizontal. It is shown analytically that axial velocity of the s tring influences the peak amplitude of the string vibration at the pas sage through resonances. Moreover, it is shown numerically that the am plitudes of both the string and the mass vibrations depend on the sign of the axial velocity, when the natural frequency of the mass-spring system is close to the frequency of the excitation. The above two theo retical results are confirmed experimentally with a simple experimenta l setup.