A $70\mathrm{.}7-kg$ 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 $k=3060\frac{N}{m},$ and the vertical distance between the highest and lowest points in the motion is $0\mathrm{.}216$ m $.($a$)$ What is the amplitude of the motion? $($b$)$ Starting when the diver is at the highest point, what is his speed onequarter of a period later? $($c$)$ If the vertical distance between his highest and lowest points were changed to $0\mathrm{.}146$ m $,$ what would be the time required for the diver to make one complete motional cycle?