Category: Differential Equations

Categories
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) .

Categories
Calculus Differential Equations Math ODE

What is a Differential Equation?

Lots of calculus students learn to solve differential equations without understanding what they really mean. Here’s a simple example of a differential equation so you can see how it works.