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1. Suppose a system has a potential energy: $U=A(x_{2}?R_{2})_{2}$ where $A$ is a constant and $R$ 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 $x$ such that all equilibria are clearly visible. (b) Consider a particle at a position $x=R+dr$ (where $dr$ 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 $x=R+dr$ at $t=0$. Describe the subsequent motio $x(t)$, in terms of $R,A$, and $dr$. If (for instance) the motion is periodic, be sure to give the angular frequency.

Given: potential energy, U=A(x2?R2)2where, A and R are both constants

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