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A particle, of mass m, is moving in one dimension under the influence of a conservative
force with potential V (x).
(a) If the potential is given by
V (x) = x² – x*,
(2)
-
find any equilibrium points and determine their stability.
(b) The particle is started from the origin x = 0 with speed v, and moves under the
influence of the potential V (x) defined in equation (2). How large does v need to be
for the motion to be unbounded?

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