Conservation of Energy

• Make free-body diagrams of a mass oscillating up and down on the end of a spring for three situations: equilibrium, accelerating up, and accelerating down.  Label the forces using mg and ky, the magnitude of the spring force.  Also indicate if the situation corresponds to the top, middle, or bottom of the oscillation.
  
  
• If the zero of the potentials is the unstretched position of the spring, write out the gravitational and spring potentials, as well as the kinetic energy, for the top, middle, and bottom, of the oscillation.  Use the variables m (mass), g (magnitude of gravitational acceleration), y_t, y_m, y_b (y-positions), v_m (speed at middle), and k (spring constant), where the subscripts refer to top, middle, and bottom.  The positive direction of the coordinate system that we are using is up.
  
  
•  Write the total mechanical energy (kinetic plus potentials) for each of the three situations:  top, middle, and bottom.