[geocentrism] on physics.
- From: "philip madsen" <pma15027@xxxxxxxxxxxxxx>
- To: <geocentrism@xxxxxxxxxxxxx>
- Date: Thu, 21 Aug 2008 15:56:25 +1000
http://dev.physicslab.org/TOC.aspx
this is a neat resource with neat lessons and links within links to lose you ..
but worth a visit.. The Math can be a bit deep for me and some.. but is not a
distraction.
Philip
a short sample ...
Resource Lesson
Period of a Pendulum
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A simple pendulum consists of a string, cord, or wire that allows a
suspended mass to swing back and forth. The categorization of "simple" comes
from the fact that all of the mass of the pendulum is concentrated in its "bob"
- or suspended mass.
As seen in this diagram, the length of the pendulum is measured from the
pendulum's point of suspension to the center of mass of its bob. Its amplitude
is the string's angular displacement from its vertical or its equilibrium
position. If a pendulum is pulled to the right side and released to swing back
and forth, its path traces our a sine curve as shown below.
The time required for one complete vibration, for example, from one crest
to the next crest, is called the pendulum's period and is measured in seconds.
The formula to calculate this quantity is
where
a.. L is the length of the pendulum in meters
b.. g is the gravitational field strength, or acceleration due to
gravity
This quantity at sea level is 9.81 m/sec2 and can be calculated as
where
a.. G = 6.67 x 10-11 nt m2/kg2
b.. M Earth is the mass of the earth (6.02 x 1024 kg)
c.. R Earth is the average radius of the earth (6.4 x 106 meters)
Notice in the formula that the mass of a simple pendulum's bob does not
affect the pendulum's period; it will however affect the tension in the
pendulum's string.
In this related lesson, you will find a derivation of this formula for
the period of a simple pendulum that will help you understand the restrictions
on its use. It will also explain to you why a simple pendulum is NOT a true
representation of simple harmonic motion, SHM. Take a few moments and use this
physlet to investigate how the period of a pendulum is impacted by its length
and its initial displacement.
The frequency of a pendulum represents the number of vibrations per
second. This quantity is measured in hertz (hz) and is the reciprocal of the
pendulum's period.
Let's practice a few problems with these formulas.
What would be the period of a pendulum located at sea level if it
is 1.5 meters long?
If the pendulum's length were to be shortened to one-fourth its
original value, what would be its new period?
How many complete vibrations would this shorter pendulum trace
out in one minute if it were to be released with a small initial amplitude?
At sea level, how long would a pendulum be if it has a frequency
of 2 hz?
The timing mechanism in a grandfather's clock is based on the
principles of a simple pendulum. If your clock is gaining time, should you
shorten or lengthen its pendulum?
Would a grandfather clock keep time on the moon?
snipped 
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