Physical pendulum with air friction

[congman]

Homework Statement

For my control system course i need to derive differential equation and period of a physical pendulum.
Pendulum rod's mass is m, length is l and has a spherical mass M

Homework Equations

i need relevant equatins so obviously :D

The Attempt at a Solution

i know that i should use stoke's equation for air firicition but i couldn't find out how.
in some posts period of a physical pendulum is given but i need to solve max. angle

Thank andd sorry about my crappy englisf.İ hope i can define my question

 

[blochwave]

http://hyperphysics.phy-astr.gsu.edu/hbase/pendp.html#c1

Learn this first, then worry about the air friction, if you're in a course that's apparently wanting you to use an advanced differential equation and you're asking for pendulum equations, you probably need to do some reading

 

[congman]

i know the pyhsical pendulum. İ do not need to solve differantial equation.İ just need to derive it.İ find a lot of sources about it but none of them include air friction.
and thaks for the reply

 

[blochwave]

Oh ok

Well the Navier Stokes equation itself deals with the air friction(it's a fluid flow equation so let's say "viscosity")that's what the equation is for

The best I can offer beyond that is this

http://en.wikipedia.org/wiki/Navier-Stokes_equations#Derivation_and_description

 

[HallsofIvy]

You probably don't have to go back to "Navier-Stokes". Generally speaking, friction can be modeled by $-k dy/dx$ or $-k(d^2y/dx^2)$. Which do you think is approriate here?

 

[congman]

i think -k.v is more approriate for my case

 

[blochwave]

If it's a control systems course I wouldn't put it past an engineering demon professor to have required it with navier stokes. But yah, if they just said model air friction, throwing in a velocity or velocity squared dependent force makes it plenty difficult I'd think

 

[congman]

This is the differential equation of a physical pendulum with no air friction.
In my case there will be a force because of friction and it will be -k.v

My problem is how to include this force to the dif. equ. and what will be the k?