Which is true about the total mechanical energy of a pendulum in the absence of friction? a. it is conserved when pe = ke. b. it is conserved when pe > ke. c. it is conserved when pe < ke. d. it is conserved for all positions of the pendulum.

option D. it is conserved for all positions of pendulum.

That is a basic principle that you can use in all physics problems: neglecting the friction, and other forms of energy, mechanical energy is conserved.

In the pendulum, the relevant energy forms are potential energy (PE) and kinietic energy (KE), which constitutes the mechanical energy (ME):

ME = PE + KE

When the pendulum starts from its higher position, at rest, all the mechanical energy is potential energy. As the pendulum moves (rotating around the pivot) it loses height (potential energy) and gains speed (kinetic energy). At the lowest point the speed is maximum and all the potential energy has been transformed into kinetic energy.

The transformation of kinetic energy into potential energy (and viceversa), keeping the total mechanical energy, is continuous, and under the absence of friction, never ends, being the mechanical energy conserved for all the positions.