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In this study a new approach to the problem of transverse vibrations of anideal string is presented. Unlike previous studies, assumptions such asconstant tension, inextensibility, constant crosssectional area, smalldeformations and slopes are all removed. The main result is that, despite suchrelaxations in the model, not only does the final equation remain linear, but,it is exactly the same equation obtained in classical treatments. First, an"infinitesimals" based analysis, similar to historical methods, is given.However, an alternative and much stronger approach, solely based on finitequantities, is also presented. Furthermore, it is shown that the same resultcan also be obtained by Lagrangian mechanics, which indicates the compatibilityof the original method with those based on energy and variational principles.Another interesting result is the relation between the force distribution andstring displacement in static cases, which states that the force distributionper length is proportional to the second spatial derivative of thedisplacement. Finally, an equation of motion pertaining to variable initialdensity and area is presented.

Variable Tension, Large Deflection Ideal String Model For Transverse Motions