Variations of Initial Shape of Deflection of a Stretched String

Abstract

In this paper, One-dimensional wave equation is formulated by applying the Newton’s second law of motion. Employing the one dimensional wave equation, speeds of decay of vibration deflection distribution in initially triangular shape of a string stretched at both ends are analyzed. Eigenfunction and the corresponding Eigenvalues with the various inclination of initial position of the string are found. The frequencies of the vibrations are analyzed from the Eigenvalues and Eigenfunction with different mass of the string. The initially triangular shape string is varied for analyzing the deflection of the string. The deflection of a string distribution withm different initial triangular shape positions of the string is analyzed. Finite difference method is applied to find the deflection distribution numerically. Deflections of the string with the different mass and tension forces in the different time interval are observed.