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PHY 232
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I have a question about Class Notes #13.
I understand that T is inversely proportional to L. In the first table, I am confused as to where the values for L came from (64,32,16cm, etc.) How were those calculated?
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You might want to review simple harmonic motion from first semester.
The simple harmonic motion of an object of mass m subject to a net restoring force F_net = - k x is modeled by a point moving about a reference circle with angular velocity omega = sqrt(k / m).
For a pendulum, analysis of the tension vector reveals that k = m g / L, so for the pendulum omega = sqrt(k / m) = sqrt( (m g / L) / m) = sqrt(g/L).
Thus the period is 2 pi / omega = 2 pi / (sqrt(g / L) ), which in simplified form would be 2 pi sqrt(L / g).