Elliptic Functions 1.1

For fixed k, Flk has an inverse denoted by sn(k, u), that satisfies u = Flk(), if and only if sn(k, u) = sin(). The function sn(k, u) is called a Jacobi elliptic function and has many properties that resemble those of the sine function. Using the Jacobi elliptic function sn(k, u), express the equation of motion for the pendulum in the form B = 2arcsinksn[k, (T P)/4], where T = 2π√(l/g) and P = t/T. Take l = 1m, g = 9.8 m/sec^2, and π/4 radians. Use Runge Kutta algorithms or tabulated values

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