Answer Happy

Problem 2: Spring boundary condition We derived the equation of motion for vibration of a string in the class using the extended Hamilton principle. Let's redo the calculation for a different boundary condition. Consider a string of constant mass per unit length p. u(x, t) I X constant tension T, and length L clamped at x = 0. There is no distributed load acting on the string. At x = 4, the string is connected to the ground by a spring with spring constant k. When the string is not vibrating, the spring is unstretched. Derive the equation of motion for the transverse displacement of the string u(x, t) using the extended Hamilton principle. Clearly state the boundary conditions of the problem.