2008-Will-Hansen-ExamplesOfODEsInPhysics

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Abstract

Witt-Hansen, Ole. 2008. Examples of the Differential equations of Physics. www.olewitthansen.dk.

 

Contents

1. The dependence of pressure with altitude.............................................................................. 1

2. Radioaktive chains of decay .................................................................................................. 3

3. Linear motion of a particle in liquids and gasses................................................................... 6

3.1 A ball sinking in a liquid...................................................................................................... 6

3.2 Vertical motion with turbulent resistance in liquids and gasses .......................................... 8

3.2.1 Upward movement ............................................................................................................ 9

3.2.2 Downward movement: .................................................................................................... 11

3.2.3 Vertical motion in air ...................................................................................................... 11

4. The motion of a projectile .................................................................................................... 13

4.1 The motion of a projectile without drag............................................................................. 13

4.2 The motion of a projectile with drag (air resistance) ......................................................... 14

5. Damped harmonic oscillations............................................................................................. 16

5.1 Solution to the differential equation using complex numbers. .......................................... 17

5.2 Traditional solution of the same differential equation .......................................................19

6. Forced harmonic oscillations without damping ................................................................... 21

7. Numerical solution to differential equations........................................................................ 24

7.1 Taylor’s formula ................................................................................................................ 24

7.2 Numerical solution to first order differential equations..................................................... 25

 

Key words: differential equations, physics, harmonic oscillator, projectile, motion, resistance, radioactivity

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Researchers should cite this work as follows:

  • Brian Winkel (2018), "2008-Will-Hansen-ExamplesOfODEsInPhysics," https://simiode.org/resources/5796.

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