# A particle that can move along the x-axis is part of a system with potential energy U(x) = A x 2 − B x , where A and B are positive constants. (a) Make a sketch of U(x) vs x.(b) Where are the particle’s equilibrium positions? (You may neglect the “point” where x is very large)(c) Describe how a particle would move if given small displacements from the equilibrium positions. For each of the points you identified in Part A, identify if it is a point of stable or unstable equilibrium.

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A particle that can move along the x-axis is part of a system with potential energy U(x) = A x 2 − B x , where A and B are positive constants. (a) Make a sketch of U(x) vs x.

(b) Where are the particle’s equilibrium positions? (You may neglect the “point” where x is very large)

(c) Describe how a particle would move if given small displacements from the equilibrium positions. For each of the points you identified in Part A, identify if it is a point of stable or unstable equilibrium.

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Step 1

(a)

Consider the given function of the potential energy, take the values for the constants A and B as 1.

Step 2

The graph of the above function of the potential energy follows the pattern of the parent function as y=x2.

Use the transformation rule, and following table to graph the given function.

Step 3

The graph of the above function o...

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