A bead of mass m slides on a frictionless wire bent into the shape y = bcosh(x/b) , with y vertically upward and b some constant.
a) Show that the lagrangian is (1/2)m?2cosh2(x/b)-mgbcosh(x/b), with x as the generalised coordinate.
b) Use the lagrangian method to generate a differential equation of motion.
c) For small oscillations, approximate the differential equation (expand in Taylor series), neglecting terms higher than first order in x and its derivatives. Find the period of small oscillations.