The total energy is: EKinetic + EPotential = Etotal 1) 1/2*mv2 +
1/2*kxmax2 = Etotal When the spring is fully compress the
kinetic energy is zero and so the potential energy is equal to
the total energy: 2) 1/2*kxmax2 = Etotal When the spring is not
compress at all, the potential energy is zero, which results in
the kinetic energy being a maximum, which requires the velocity
to be a maximum as well. The velocitiy at any given point, such
as in part d) can be solved by evaluating equation 2) to get the
total energy, algebraically solving equation 1) for velocity, v.
Once the velocity is known the knietic energy can be directly
evaluated.