A particle executes simple harmonic motion with amplitude A and period T. Consider the region located between x=−x1 and x=+x1, where 0<x1<A.
a. (a) Derive an expression for the time taken by the particle to travel from x=−x1 to x=+x1 through the mean position.
b. (b) Hence obtain an expression for the total time during one complete oscillation in which the particle remains inside the band ∣x∣<x1.
c. (c) For x1=2A, calculate the ratio of the time obtained in part (b) to the period T. State the result in its simplest form.