Simple harmonic motion and cursed a buoy?
A buoy oscillates in simple harmonic motion Acosw = (w) t as waves move past. The buoy moves a total of 3.5 feet (Vertical) from its lowest to its climax. Back to its highest point in 10 seconds. A) Write an equation that describes the movement of the buoy if it is in its peak at t = 0. B) Find the velocity of the buoy as a function of t. c) Determine the time when the speed of the buoy is higher. What is the speed these days? I've never seen this before in my life, please help!
The amplitude is half the distance from the lowest point to point higher. That's 1.75ft. The oscillation period is 10 sec. W = 2pi / 10 = pi / 5. (A) The equation of motion with and in feet and t in sec.is therefore: y = 1.75 cos (pi / 5) t. (B) The velocity v is: dy / dt – (1.75pi / 5) sin (pi / 5) t = – 0.35pi (sin pi / 5) t / m sec. (C) v = when you: dv / dt = 0 – (1.75pi ^ 2 / 25) cos (pi / 5) t = 0 t pi / pi + 5 = 2n / – pi / 2 for any integer nt = 10n + / – 5 / 2 sec positive values of t are: / 2 5 sec ., and every 5 sec. to thereafter.
Buoy Removal
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