A research team sets up two identical pendulums, each consisting of a small dense bob suspended by a light, inextensible string of length 1.50 m. One apparatus operates in a laboratory on Earth where the local gravitational field is 9.80 m/s²; the other operates inside a sealed chamber on Mars where the gravitational field is 3.70 m/s². For both pendulums the initial angular displacement is less than 5°, so their motion remains within the small-angle regime.
(a) Qualitatively compare the time required for one complete oscillation (period) of the two pendulums. Identify which pendulum has the longer period and explain your reasoning without performing numerical calculations.
(b) Without explicit calculation, describe how the oscillation frequency of each pendulum compares to the other and justify your answer.
(c) An engineer suggests increasing only the mass of the bob on the Martian pendulum to shorten its period. Explain whether this modification will achieve the desired effect for small-angle oscillations, citing appropriate physical reasoning.
(d) Describe how doubling the length of the Earth pendulum would affect its period and its frequency. Support your answer using proportional reasoning.