Determine the frequency of vertical oscillations about the equilibrium position in Problem...

Determine the frequency of vertical oscillations about the equilibrium position in Problem

Problem

A light elastic cord of length 2land stiffness kis held with the ends fixed a distance 2lapart in a horizontal position. A block of mass m is then suspended from the midpoint of the cord. Show that the potential energy of the system is given by the expression

where y is the vertical sag of the center of the cord. From this show that the equilibrium position is given by a root of the equation

where u = yll and a = mg/4kl.