Frequency Response of a Nonlinear Stretched String

The problem of the forced vibration of an elastic string with variable tension is considered. All equation of motion is given for the case of low amplitude motion, but for strings of high modulus for which it is shown that tension variations are an important source of nonlinearity. An exact solution is obtained by assuming as a driving function a Jacobean elliptic function of the cosine type. Tension variations and amplitude are calculated as functions of frequency. Experimental results are presented and compared with the theory.