Mass on a Stick Model: Solve for Realistic Results

[Integral]

I have need of a mathematical model of a mass at the end of a stick, pivoting about the opposite end. What I have done so far is not giving realistic results, would appreciate it if some one could point out my error.

Basic model :

\tau = I \ddot {\theta}

I = m r^2

The system is being pushed by an air cylinder (force F) with the fixed end mounted a distance L directly below the pivot, the moving end of the cylinder is mounted a distance r along the pivot arm from the pivot point. With \phi the angle between the cylinder and the pivot arm. So I have :

\tau = r F sin( \phi)

My variable of interest will be the angle between the pivot arm and the line defined by the pivot and the fixed end of the cylinder, call this angle \theta

By the law of sines I get

\frac {Sin(\phi)} {L} = \frac {sin(\theta)} {x}
where x is the length of the cylinder.

I get x in terms of \theta from the law of cosines

x^2 = L^2 + r^2 -2lr cos(\theta)

The differential equation is:

\ddot{ \theta } = \frac { \tau } {I}

See the attachment for a diagram.

 

[Integral]

Ok, The above model is correct. For the last week I have been running this through an excel spreadsheet using a Runga Kutta method, the results were not correct, the system simply did not respond the way I KNEW it should.

My error? using the fricking English measurement system. I was using lbs where I needed slugs. So I was throwing 32 times the mass I thought I was. That sort of slowed things down. I finally made the simulation work by changing everything to metric, Newtons for force, kg for mass and meters everywhere, It worked great. It was then that I seriously began to figure out the lbs mass lbs force issue.