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Calculus Differential Equations Physics Science

Physics Pendulum Problem

Getting the Period of a Spring-Operated Physical Pendulum

A juicy physics problem that requires delving into the differential equation for pendulum motion. A rod of mass M on a pivot a distance r from the end is driven by a spring of constant k pulling the end back and forth to make an (admittedly stupid) physical pendulum. We have to show that its period T is given by T^2 = 4\pi \frac{M}{3kr^2} (L^2 + 3r^2 -3rl) .

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