The potential energy of a mass m a distance r from the origin is: h2 U(r) : r2 for 0
The potential energy of a mass m a distance r from the origin is: h2 U(r) : r2 for 0
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Transcribed Image Text:The potential energy of a mass m a distance r from the origin is:
h2
g?
+
r2
U(r):
for 0 < r < o∞, with g and h positive constants.
(a) Find the equilibrium position ro. Is this a point of stable or unstable equilib-
rium ? For credit, prove why.
(b) Let x be the displacement from the equilibrium position. For small x (x << ro),
what is the frequency of oscillation w =
Vk/m ? Express your answer in terms of
g, h, m, and numerical terms.
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