Final answer:
The new frequency of the simple harmonic motion when a 75.0-kg diver is on the diving board is 2.67 Hz, as the frequency decreases with an increase in the combined mass of the system.
Step-by-step explanation:
The frequency of simple harmonic motion (SHM) for a diving board with an attached diver can be calculated using the formula for the frequency of a mass-spring system: f = \( \frac{1}{2\pi} \sqrt{\frac{k}{m}} \),
where f is the frequency, k is the spring constant, and m is the combined mass of the diver and the diving board. Since the spring constant remains the same and the initial frequency with only the board was 4.00 Hz, we can deduce that the frequency will decrease when the mass is increased by adding the mass of the diver. Using the concept of direct and inverse proportionality, the new frequency can be found by the square root of the ratio of the initial mass to the final mass times the initial frequency, which comes to 2.67 Hz for the additional mass of the diver (75.0 kg).