In this work we solve the nonlinear second order differential equation of the
simple pendulum with a general initial angular displacement
(θ(0)=θ0​) and velocity (θ˙(0)=ϕ0​), obtaining a
closed-form solution in terms of the Jacobi elliptic function sn(u,k),
and of the the incomplete elliptical integral of the first kind F(φ,k).
Such a problem can be used to introduce concepts like elliptical integrals and
functions to advanced undergraduate students, to motivate the use of Computer
Algebra Systems to analyze the solutions obtained, and may serve as an exercise
to show how to carry out a simple generalization, taking as a starting point
the paper of Bel\'endez \emph{et al} \cite{belendez}, where they have
considered the standard case θ˙(0)=0