### Re: Pendulum: What is relationship of the T^2 vs. length?

Date: Fri Jan 3 13:34:15 2003
Posted By: Chris Seaman, Staff, Electrical Engineering, Materials Engineering, Alcoa Technical Center
Area of science: Physics
ID: 1040742124.Ph
Message:
```
Michael,

Your thinking is not "off".  In terms of simply solving an algebraic
problem, you are correct.

But now, step back and look at the problem a little bit differently.
Let's assume you don't know anything about pendulums and want to perform
an experiment in which you vary the pendulum length, L, the mass, and the
starting position.  You also have the ability to measure the period
accurately.  (You may do this by measuring one period, or taking the
average of many periods).  You would find that T^2 is directly
proportional to the pendulum length, and completely independent of the
mass or the starting position (as long as the starting position
wasn't "too high").

You now have a simple device that can accurately measure time, and is
quite easy to calibrate (adjust the length) and keeps accurate time even
as the power "runs down".  This type of understanding of mechanisms is
what lead to the development of portable, accurate clocks, which
revolutionized navigation in the 17th Century.

One goal of this type of physics analysis and experimentation is to
develop an understanding of unique relationships between phenomena, and
convert it into a mathematical model, if possible.  Even at this moment,
researchers in nanotechnology are using this type of modeling to develop
new sensors and devices.

Solve a problem, then step back to try to understand what the solution
means.

Christopher M. Seaman
Technical Specialist
ALCOA Technical Center

```

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