Final answer:
The pendulum with the greatest frequency is the one with the shortest length. As for adjustments when the acceleration due to gravity changes, the pendulum should be shortened to keep the correct time. Amplitude refers to maximum displacement and is unrelated to frequency.
Step-by-step explanation:
The pendulum with the greatest frequency is the one with the shortest length. The frequency of a pendulum, which is the number of oscillations it makes per unit time, is inversely proportional to the square root of its length. According to the formula for the period of a simple pendulum (T = 2π√(L/g)), where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity, a shorter pendulum will have a smaller value for T and consequently a higher frequency, since frequency is the reciprocal of the period (f = 1/T).
When moving to a city where the acceleration due to gravity is slightly greater, you would need to shorten the pendulum in your clock to maintain the correct time. This is because a greater acceleration due to gravity decreases the period of the pendulum, making the clock run faster, hence the need to reduce the length to increase the period back to the correct value.
The amplitude of a pendulum's motion, which refers to the maximum displacement from the equilibrium position, will be larger for the pendulum that is displaced farther from its equilibrium position initially, but it does not affect the frequency.