Question

(30 Points) 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 frequency of the buoy is ¼ (it completes ¼ of a cycle every second).
a. What is the amplitude of the function that models the buoy's motion?



b. What is the period of the function that models the buoy's motion?



c. Using cosine, write a possible equation to model the motion of the buoy

Explain your answers please

Answer 1

Answer:  a) A = 3

               b) P = 4

               c) $\bold{3\ cos\dfrac{\pi}{2}x}$

Step-by-step explanation:

$Amplitude (A) = \dfrac{max-min}{2}\\\\\\.\qquad \qquad \qquad =\dfrac{6}{2}\\\\\\.\qquad \qquad \qquad =\boxed{3}$

Period (P) is the reciprocal of the frequency (f)

f = $\frac{1}{4}$   →    P = $\frac{4}{1}\quad =\boxed{4}$

y = A cos (Bx - C) + D

• A = 3
• $P=\dfrac{2\pi}{B}$    →  $4=\dfrac{2\pi}{B}$     →     4B = 2π     →    $B=\dfrac{2\pi}{4}$   →   $B=\dfrac{\pi}{2}$
• C = none given
• D = none given

$\large{\boxed{y=3\ cos\dfrac{\pi}{2}x}}$