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The simple pendulum usually studied by analytic methods invokes the small angle approximation (SAA) so that one can easily reduce the equation of motion to Hooke’s law and thereby obtain the period of the pendulum and other associated quantities. If the approximation is relaxed, the problem becomes analytically intractable and one must resort to computational methods. In this exercise, the pendulum with and without the SAA are compared to allow students to discover what happens to the temporal behavior for larger angles of displacement. The students will also be able to obtain quantitative estimates of what a “small angle” means, and the limits of validity of the SAA. In the computations, students will learn that the second order differential equation that describes the motion of the pendulum can be reduced to two coupled first order differential equations, which can then be solved by the Euler-Cromer algorithm. In this specialized exercise set, students will also learn to use the ODE45 package in MATLAB to solve differential equations and its advantages over Euler-Cromer method, as well as ‘findpeaks’ command in MATLAB.