# Physical pendulum with air friction

1. Jan 7, 2008

### congman

1. The problem statement, all variables and given/known data

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

2. Relevant equations

i need relevent equatins so obviously :D

3. The attempt at a solution

i know that i should use stoke's equation for air firicition but i couldnt find out how.
in some posts period of a pysical pendulum is given but i need to solve max. angle

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

2. Jan 7, 2008

### 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

3. Jan 7, 2008

### 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

4. Jan 7, 2008

5. Jan 7, 2008

### HallsofIvy

Staff Emeritus
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?

6. Jan 7, 2008

### congman

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

7. Jan 7, 2008

### 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

8. Jan 7, 2008

### 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?