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A large Foucault pendulum such as hangs in many science
Chapter 5, Problem 5.42(choose chapter or problem)
A large Foucault pendulum such as hangs in many science museums can swing for many hours before it damps out. Taking the decay time to be about 8 hours and the length to be 30 meters, find the quality factor Q.
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QUESTION:
A large Foucault pendulum such as hangs in many science museums can swing for many hours before it damps out. Taking the decay time to be about 8 hours and the length to be 30 meters, find the quality factor Q.
ANSWER:Step 1 of 4
Given,
decay time, \(\mathrm{t}=8\mathrm{\ hrs}=8\times3600=28.8\times10^3\mathrm{\ s}\)
Length of pendulum, \(\mathrm{l}=30\mathrm{\ m}\)
The quality factor is given by,
\(Q=\frac{\omega_{0}}{2 b}\)
Where \(2 \beta\) is the full width half maximum and \(\omega_{0}\) is the natural frequency of the oscillator.
\(\beta\) is inversely proportional to decay time \((\mathrm{t})\).
That is,
\(\beta=\left(\frac{1}{\tau}\right)\)
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