Question

Due to tides mean sea level off of Newport Beach reaches a height of 1.3 meters during high

tide and 0.3 meters during low tide. Successive high tides occur every 12 hours (43,200

seconds). A buoy with mass m = 40 kg is floating in the ocean off of Newport Beach.

1) Relevant concepts/equations. (5 points.)

2) Assume we begin to measure the buoy’s displacement at High tide which occurs exactly

at 12:00 am (0 seconds). Also assume we can model the buoy’s displacement as a simple

undamped oscillation. What is the amplitude and phase angle for the buoy’s

displacement? (10 points)

3) During one half cycle of six hours (21600 seconds), the buoy’s displacement passes

through an angle of 180 degrees. From this information, what is the angular frequency ω of the buoy? (5 points)

4) Using your previous answer, what is the force constant ‘k’ acting on the buoy? (5 points)

5) What is the maximum velocity of the buoy? What is the maximum acceleration of the

buoy? (10 points)

6) What is the energy of the buoy due to tidal displacement? (5 points)

7) How much work is done during one low tide to high tide cycle? How much Power per

hour is required to accomplish this? (Assume g= 9.81m/s^2 , compare your answer to a 65W light bulb which uses 65 watts per hour.)

Answer 1

1) We can model the motion of the buoy as a simple harmonic motion, its vertical displacement as a function of time has a sinusoidal shape. Since the buoy moves between 0.3m and 1.3m height, this means that the equilibrium point is at 0.8m and the maximum displacement (amplitude of the motion) is 0.5m. The period of the motion (time it takes to complete 1 cycle) is equal to 43,200s.

2) For t=0s y=1.3m, then:

3) The angular displacement is:

4) The relationship between the angular frequency and the force constant is:

5) The maximum velocity and the maximum acceleration are given by:

6) The energy of the buoy due to tidal displacement is:

7) The work done in going from low tide to high tide is:

The power requirement is: