(a) Explanation Given information: The equation of force ( F ) is F = k 1 x − k 2 x 3 . Calculation: Write the general expression for calculating the potential energy as follows: V = 1 2 k x 2 Calculate the work done ( U 1 − 2 ) using the relation: U 1 − 2 = − ∫ x 1 x 2 F d x Substitute k 1 x − k 2 x 3 for F . U 1 − 2 = − ∫ x 1 x 2 ( k 1 x − k 2 x 3 ) d x = − [ k 1 x 2 2 ] x 1 x 2 + [ k 2 x 4 4 ] x 1 x 2 = − [ k 1 2 ( x 2 (b) To determine Find the maximum velocity ( v ) of the particle of mass m attached to the spring and released from rest with x = x 0 .

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Chapter 13.2, Problem 13.84P

(a)

To determine

Find the potential energy Ve as a function of x.

(b)

To determine

Find the maximum velocity (v) of the particle of mass m attached to the spring and released from rest with x=x0.

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Chapter 13.2, Problem 13.83P

Chapter 13.2, Problem 13.85P

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Find the potential energy V e as a function of x .

Solution Summary: The author explains how to find the potential energy V_e as a function of x.