Why is it safe for the man to fix his chin in a stationary position whle waiting for the pendulum bob?

Safe. The pendulum will swing away and back and will not touch his chin again. With the pendulum raised it has been given a certain amount of potential energy. When the pendulum is released the pendulum starts converting it's potential energy to kinetic energy. By the time the pendulum has reached the bottom of it's swing, it has converted all of it's original potential energy to kinetic energy, i.e. energy as result of it's motion. As the pendulum climbs up again on the other side, the reverse happens, the kinetic energy is converted into potential energy. Eventually the pendulum will stop when all of it's kinetic energy has been converted to potential energy which will be at the same height as when it was released. On the reverse swing the same thing happens so that by the time the pendulum approaches the man's chin again, the kinetic energy of the pendulum will have been converted back to potential energy, i.e. the pendulum will be virtually motionless at this point and not a danger...