4.29** [Computer] A mass m confined to the x axis has potential energy U = kx4 with k > 0. (a) Sketch this potential energy and qualitatively describe the motion if the mass is initially stationary at x= O and is given a sharp kick to the right at t = 0. (b) Use (4.58) to find the time for the mass to reach its maximum displacement xmax = A. Give your answer as an integral over x in terms of m, A, and k. Hence find the period of oscillations of amplitude A as an integral. (c) By making a suitable change of variables in the integral, show that the period 7 is inversely proportional to the amplitude A. (d) The integral of part (b) cannot be evaluated in terms of elementary functions, but it can be done numerically. Find the period for the case that m = k = A = 1.

4.29** [Computer] A mass m confined to the x axis has potential energy U = kx4 with k > 0. (a) Sketch this potential energy and qualitatively describe the motion if the mass is initially stationary at x= O and is given a sharp kick to the right at t = 0. (b) Use (4.58) to find the time for the mass to reach its maximum displacement xmax = A. Give your answer as an integral over x in terms of m, A, and k. Hence find the period of oscillations of amplitude A as an integral. (c) By making a suitable change of variables in the integral, show that the period 7 is inversely proportional to the amplitude A. (d) The integral of part (b) cannot be evaluated in terms of elementary functions, but it can be done numerically. Find the period for the case that m = k = A = 1.