solution: part b.

Now that we know the total energy of the system, we need to find the potential and kinetic energies given different angles in between the maximums. The one constant is that the total energy will never change; the sum of the PE and the KE will ALWAYS equal E.

We are given the angle tex2html_wrap_inline40 , so we start by finding the potential energy at that point, just like in part a.

eqnarray18

Now that we have an expression for the PE, we can use the fact that the sum of the KE and PE must equal the total energy of the system E.

eqnarray22

Now that we have the kinetic energy we can solve for the velocity using the definition of KE.

eqnarray24