Final answer:
The incorrect statement is that the period of a simple pendulum significantly depends on amplitude; it is nearly independent of amplitude for small angles and mainly depends on the length and acceleration due to gravity.
Step-by-step explanation:
The statement that is incorrect out of the given choices is that the period of a simple pendulum noticeably depends on the amplitude for large amplitudes. The period of a simple pendulum is nearly independent of amplitude, especially if it is less than about 15°. The period only significantly depends on the length of the pendulum and the acceleration due to gravity. It is independent of the mass of the pendulum bob. Also, it is true that a pendulum would not oscillate in a zero-g environment because it relies on gravity to create the restorative force necessary for its motion. Lastly, a damped pendulum does not have a constant period because the damping force removes energy from the system, gradually altering the motion.