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course Phy 201
11/28 6
aFor small displacement from equilibrium vector resolution of the forces tells us that the x component of tension in the same proportion to tension as the displacement x to the length L:
x / L
Since for small angles the tension is very nearly equal to the weight mg of the pendulum this gives us
Tx / m g = x / L so that
Tx = (m g / L) * x.
Since Tx is the restoring force tending to pull the pendulum back toward equilibrium we have
restoring force = k * x
for k = m g / L. So the restoring force constant is m g / L
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