IV Pendulum Study

March 26, 2009

At the March 26, 2009 Tribe Meeting

we observe the behavior of a pendulum.

video

We make measurements on the pendulum.

We use a lamp to cast a shadow on the paper.

We use a stopwatch to make measurements

of the time to complete 20 cycles.

We also notice the starting and ending positions

after 20 cycles.

I arrange the data in a table to facilitate computations.

I compute Gravity at Incline Village = at 9.77821 m/sec²

that is slightly below the standard physics number of 9.8.

Low Amplitude Model

Plugging the low amplitude values into the pendulum model,

I see the period is about right.

By trial and error, I derive on a Drag Time of 35 seconds.

High Amplitude Model

Plugging the high amplitude values into the pendulum model,

I see the period is about right.

I again use a Drag Time of 35 seconds.

Tuning-Up the Model

Low Amplitude

I zoom in on the first cycle

and take numerical measurements of the model.

IV_Pendulum/p_data_127.xls

I also decrease dt to gain more accuracy.

This indicates a Drag Time of 125 seconds.

I attribute the increase in Drag Time

to the reduction in spurious gain

from decreasing dt.

Tuning-Up the Model

High Amplitude

I zoom in on the first cycle

and take numerical measurements of the model.

IV_Pendulum/p_data_584.xls

I also decrease dt to gain more accuracy.

This indicates a Drag Time of 80 seconds.

I again attribute the increase in Drag Time

to the reduction in spurious gain

from decreasing dt.

Conclusions and Areas for Further Investigation

The measurements seem accurate enough

to support a fairly accurate derivation of G.

I suspect the longer of the two low-amplitude period measurements

is incorrect - pendulum periods grow with amplitude.

The model generates a period of oscillation

that matches that of the actual pendulum.

The Drag Time that fits the data best

changes with decreasing dt,

indicating the original dt is too large.

The necessity to decrease Drag Time from 125 to 80

as the amplitude increases from .127 m to .584 meters

indicates an opportunity to refine the formulation of Drag

that is currently proportional to velocity / Drag_time.

Other Resources

(1) Dave Stancavish Model

IV_Pendulum/pendulum20090327.pdf

Dave cites this resource:

http://sysdyn.clexchange.org/sdep/

Roadmaps/RM7/D-4455-2.pdf

"Through page 12, 2nd order feedback loops is very helpful.

4426-3's pendulum model is the basis of my model.

I hunted and pecked to get the right drag time constant."

(2) Alan Lattanner Derivation for Gravity