Elliptic integrals The period of a pendulum is given by
where ℓ is the length of the pendulum, g ≈ 9.8 m/s2 is the acceleration due to gravity, k = sin (θ0/2), and θ0 is the initial angular displacement of the pendulum (in radians). The
- a. Approximate F(0.1) 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(0.1) with an error less than 10−3?
- c. Would you expect to use fewer or more terms (than in part (b)) to approximate F(0.2) to the same accuracy? Explain.
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