contestada

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 5.5 feet from its low point to its high point, and that it returns to its high point every 8 seconds. Write an equation that describes the motion of the buoy if it is at its high point at time t = 0.

Respuesta :

Chrisnando

Answer:

[tex]d = 2.75[cos \frac{\pi}{4}]t[/tex]

Step-by-step explanation:

Let's take the equation for the height of a buoy:

d = Acos(wt)

Where[tex] A = \frac{5.5}{2} = 2.75[/tex]

(We divided by 2 because there are 2 directions for the magnitude of total displacement, which is the amplitude of a periodic function)

[tex]w =\frac{2 \pi}{T}[/tex]  where T = 8 seconds

[tex]w = \frac{2 \pi}{8} = \frac{\pi}{4}[/tex]

Lets substitute the values, in the equation, we have:

[tex]d = 2.75[cos \frac{\pi}{4}]t[/tex]

Therefore, the equation that describes the motion of the buoy if it is at its high point at time t = 0 is

[tex]d = 2.75[cos \frac{\pi}{4}]t[/tex]

Otras preguntas