Elliptic integrals The period of a pendulum is given by T

Chapter 9, Problem 77

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Elliptic integrals The period of a pendulum is given by T = 4 B / gL p>2 0 du 21 - k2 sin2 u = 4 B / g F 1k2, where / is the length of the pendulum, g _ 9.8 m>s2 is the acceleration due to gravity, k = sin 1u0>22, and u0 is the initial angular displacement of the pendulum (in radians). The integral in this formula F 1k2 is called an elliptic integral, and it cannot be evaluated analytically. a. Approximate F 10.12 by expanding the integrand in a Taylor (binomial) series and integrating term by term. b. How many terms of the Taylor series do you suggest using to obtain an approximation to F 10.12 with an error less than 10-3? c. Would you expect to use fewer or more terms (than in part (b)) to approximate F 10.22 to the same accuracy? Explain.