Part 1: Modeling

The goal of this project is to numerically calculate the vibrations of a stretched string of total mass M, unstretched length L, Young’s modulus Y, and cross-sectional area A.You will do this by modeling it as a series of N+1 point masses of mass m connected by N Hooke’s-law springs, each of equilibrium length r0and spring constant k.

Recall that the spring constant K of the overall spring is given by K=AY/L. The variables A and Y only appear in the combination AY; it is useful to define this as the “stiffness”, γAY.