A 75-kg diver is standing at the end of a diving board while it is vibrating up and down in simple harmonic motion, as indicated in the figure. The diving board has an effective spring constant of k = 4100 N/m, and the vertical distance between the highest and lowest points in the motion is 0.30 m.
Concepts: (i) How is the amplitude A related to the vertical distance between the highest and lowest points of the diver's motion?
(ii) Starting from the top, where is the diver located one-quarter of a period later, and what can be said about his speed at this point?
(iii) If the amplitude were to double, would the period also double? Explain. Calculations:
(a) What is the amplitude of the motion?
(b) Starting when the diver is at the highest point, what is his speed one-quarter of a period later?
(c) If the vertical distance between his highest and lowest points were changed to 0.10 m, what would be the time required for the diver to make one complete motional cycle?

Transcribed Image Text:

0.30 m