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 H(x , p), and describe the possible phase-space orbits for the two cases E > 0 and E < 0. (Remember that the function H(x, p) must equal the constant energy E.) Explain your answers to part (b) in terms of those to part (a).

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 H(x , p), and describe the possible phase-space orbits for the two cases E > 0 and E < 0. (Remember that the function H(x, p) must equal the constant energy E.) Explain your answers to part (b) in terms of those to part (a).

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