Sliding pendulum comes to rest through friction

As I swing this pendulum like contraption the pendulum is ejected in the horizontal position, slides along the table and then comes to rest. Given the initial height of the pendulum and the distance it slides accross the table determine the coefficient of friction between the table surface and the mass of the pendulum.

Because we need to use a conservation law we must identify initial and final states

Initial state:

Mass of pendulum at rest and at height h above table

Final state:

Mass of pendulum at rest on table after sliding a distance d

The change in mechanical energy between initial and final state goes into internal energy in the system in the form of heat and can be associated with the work don by friction. Choosing zero for potential energy at the table height and zero for internal energy as that corresponding to the internal energy of the system at the start of the experiment we have

After the brick comes to rest

Using the law of energy conservation we can write

We easily perform determine the ratio of distances to be xxx.