Aug24

March 22

section covered in text

5.2. Damped Free Vibrations

objective

to understand the effect of damping forces on free vibrations
to be able to find the equation of motion describing such force

key ideas and/or vocabulary

underdamped motion (b² < 4mk)
critically damped motion (b² = 4mk)
overdamped motion (b² > 4mk)

solved problems - using key ideas

finding equation of motion in the 3 different cases of damping, #1
application, finding the maximum displacement, #8

announcements
Homework: #2,7 (due 4/2)

QUESTION OF THE DAY

The Bay of Fundy in Canada is reputed to have the largest tides in the world, with the difference between low and high water level being as much as 15 meters. Suppose at a particular point in the Bay of Fundy, the depth of the water, y meters, as a function of time, t in hours since midnight on January 1, 1994, is given by
y=y₀ + Acos[B(t - t₀)].
a. What is the physical meaning of y₀?
b. What is the value of A?
c. What is the value of B? Assume the time between successive high tides is 12.5 hours.

SOLUTION

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SOLUTION.

a. y₀ is the depth of the water between low and high tide.
b. A is the amplitude or 7.5 meters.
c. B = 2Pi/12.5

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