Final answer:
The period of the pendulum stays the same because it does not depend on temperature.
Step-by-step explanation:
The period of a pendulum is determined by its length and the acceleration due to gravity, and is independent of factors such as mass or amplitude. Therefore, when you dip the pendulum into liquid nitrogen and the temperature drops, the period of the pendulum stays the same, option C. Temperature does not affect the length or acceleration due to gravity, so it does not change the period of the pendulum.