# Approximate vs. Numerical The Pendulum Problem

Updated: Sep 18, 2020

In this study, we will be analyzing the motion of a pendulum which is composed of a massive bob attached to a massless string suspended from a ceiling (see **Fig. (0)**). First, we will apply the dimensional analysis concept (i.e the units) to obtain estimates on the relations among physical quantities without carrying out rigorous calculations. Secondly, we will show the difficulties in obtaining an analytical solution to this, yet simple-looking, problem. However, certain approximations will help us obtain a solution in an analytical form after linearizing the equations to be solved. Then, we will solve the problem using numerical methods and contrast the results with those obtained from the linearized equation. In the final part, we will propose an analytical form as the solution to the problem which would perfectly match the numerical solution.

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