Trigonometry
posted by AwesomeGuy .
Wave Motion
A buoy oscillates in simple harmonic motion as waves go past. At a given time it is noted that the buoy moves a total of 3.5 feet from its low point to its high point, and that it returns to its high point every 10 seconds. Write an equation that describes the motion of the buoy if it is at its high point at t=0.
(Note: Rationalize and think thoroughly throughout this solving process, don't stress your mind in a negative way. Just relax and look over the information carefully.)

since the amplitude is half the (maxmin), and it oscillates about the middle, we can get that by using
y=7/4 cos(t) + 7/4
since cos(t) starts out at its max at t=0. But, that has period 2π. We're almost there. We want a period of 10, so since cos(kt) has period 2π/k,
y = 7/4 cos(2π/10 t) + 7/4
is our function.
Respond to this Question
Similar Questions

Calc
A buoy oscillates in simple harmonic motion as waves go by. The buoy moves a total of 3.5 feet from its low point to its high point and it returns to its high point every 10 seconds. What is the equation that describes this motion … 
math
The angle of elevation from a buoy to the top of a bridge is 19 degrees. The bridge is 150 feet high. How far from the foot of the bridge's pillar is the buoy? 
Precalc
I am having trouble figuring out this question Jan observes a buoy bobbing up and down through a total amplitude of 8 feet. Beginning at the top of the wave, if the buoy completes a full cycle every 8 seconds, what is the height of … 
Physics
A cylinder shaped buoy is stationary out on a lake. The height of the buoy is 1 m and the diameter is 30 cm and it‘s mass is 50 kg. Now a whale swims under the buoy and hit it. The buoy raises up and begins to oscillate. a) Find … 
physics
A buoy oscillates in simple harmonic motion according to the motion of waves at sea. An observer notes that the buoy moves a total of 6 feet from its lowest point to its highest point. The buoy returns to its highest point every 15 … 
physics
A buoy oscillates in simple harmonic motion according to the motion of waves at sea. An observer notes that the buoy moves a total of 6 feet from its lowest point to its highest point. The buoy returns to its highest point every 15 … 
Math
Your fishing bobber oscillates up and down from the current in the river in a harmonic motion. The bobber moves a total of 5.0 inches from its high point to its low point then returns up to the high point every 5 seconds. Write an … 
Physics
A lobsterman’s buoy is a solid wooden cylinder of radius r and mass M. It is weighted at one end so that it floats upright in calm sea water, having density. A passing shark tugs on the slack rope mooring the buoy to a lobster trap, … 
calculas
A buoy oscillates in simple harmonic motion y = A cos(ωt) as waves move past it. The buoy moves a total of 2.7 feet (vertically) from its low point to its high point. It returns to its high point every 18 seconds. (a) Write an … 
Physical Science 8th Grade
1. What is the resulting direction of a surface wave?