Question

A buoy, floating in a ripple tank, is at rest when a wave reaches it. The wave has a frequency of 1.25 Hz, and an amplitude of 0.75 m. What is the magnitude of the buoy’s displacement after 2.20 seconds?

Answer 1

Answer:

   y = -6.57 10⁻³ m

Explanation:

The movement of water is an oscillation in the vertical direction that can be approximated as a simple harmonic movement

           y = A cos (wt)

where the amplitude is A = 0.75 m and the angular velocity is related to the frequency

            w = 2π f

            w = 2π 1.25

            w = 7.85 rad / s

we substitute

            y = 0.75 cos (7.85 t)

we look for the amplitude for a time of t = 2.20 s, remember that the angles are in radians

            y = 0.75 cos (7.85 2.20)

            y = -0.00657 m

            y = -6.57 10⁻³ m