A particle of mass m is constrained to lie along a frictionless, horizontal plane subject to a force given by the expression F(x) = -kx. It is projected from x 0 to the right along the positive x direction with initial kinetic energy To 1/2 kA". k and A are positive con- stants. Find (a) the potential energy function V(x) for this force; (b) the kinetic energy, and (c) the total energy of the particle as a function of its position. (d) Find the turning points of the motion. (e) Sketch the potential, kinetic, and total energy functions. (Optional: Use Mathcad or Mathematica to plot these functions. Set k and A each equal to 1.) 2.4

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