If a pendulum is not pushed, why does it not go as big when it swings back. Where does the lost PE go?

ans. Since there is no force applied to the pendulum there is not enough Kinetic energy (energy of motion) to transform into potential energy to make it swing back. The pendulum will not swing back as high due to gravity which will push the pendulum down. The lost PE is stored in the pendulum and makes it stationary until it is pushed.