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Consider a mass m confined to the x axis and subject to a
Chapter 13, Problem 13.28(choose chapter or problem)
Consider a mass m confined to the x axis and subject to a force Fx = kx where k > 0. (a) Write down and sketch the potential energy U(x) and describe the possible motions of the mass. (Distinguish between the cases that E > 0 and E < 0.) (b) Write down the Hamiltonian 3-4x , p), and describe the possible phase-space orbits for the two cases E > 0 and E < 0. (Remember that the function J-C(x, p) must equal the constant energy E.) Explain your answers to part (b) in terms of those to part (a).
Questions & Answers
QUESTION:
Consider a mass m confined to the x axis and subject to a force Fx = kx where k > 0. (a) Write down and sketch the potential energy U(x) and describe the possible motions of the mass. (Distinguish between the cases that E > 0 and E < 0.) (b) Write down the Hamiltonian 3-4x , p), and describe the possible phase-space orbits for the two cases E > 0 and E < 0. (Remember that the function J-C(x, p) must equal the constant energy E.) Explain your answers to part (b) in terms of those to part (a).
ANSWER:Step 1 of 3
(a)
Integrating the force from the problem we find
Refer to figure below. If the particle in question has energy then it can cross the origin. If it has energy then it cannot cross the origin.