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# (Solved): 1. Suppose a system has a potential energy: U=A(x2R2)2 where A is a constant and R is some fixed ...

1. Suppose a system has a potential energy: where is a constant and is some fixed distance from the origin (on the positive and negative side) (a) Sketch the potential energy, and identify all equilibria. Are they stable or unstable. Note: Please try to sketch it over a range in such that all equilibria are clearly visible. (b) Consider a particle at a position (where is assumed to be small). What is the forc on the particle? Be sure to include the direction. (c) Suppose a particle is released from rest at at . Describe the subsequent motio , in terms of , and . If (for instance) the motion is periodic, be sure to give the angular frequency.

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