Question

Consider the potential energy described in problem 1.14. For low amplitudes, the motion of the object is well described by simple harmonic motion, so that the period is independent of amplitude. However, once the amplitude gets high enough this is no longer true. As the amplitude increase, does the period increase or decrease? Explain your reasoning thoroughly, and assume that the amplitude is always less than pi/B.

(You do not need to answer question 1.14)

1.13 In research-level theel pnysles, I IS anoo exact solution because of the complexity of the problems being consider e appropriate approximations, so as to get e approximations f the Therefore, it is essential to mak physical insight. The Taylor series is central to many of thes You have already seen two of the three most common applications o Taylor series: sin θ θ(for small θ) and cos θ 1 In this problem, you will demonstrate the third of the three most common 2 --(for small θ). applications. Show that (1 +p"- nx for x < I. (Note that this works 1.14 The potential energy for a particular object is U (x) =-L cos fix, where L 2 whether n is positive or negative, integer or fractional.) and B are both >0. (This potential energy function is important in the study of superconductivity.) 2T 2π (a) Make a sketch of this potential energy fromx Indicate the scale on the vertical axis. tox+

Answer 1