Section 4.12

Section 4.12 A Closer Look at Forced Mechanical Vibrations

objective

to be able to determine the equation of motion of a mass attached to a spring with periodic forcing term
to be able to determine the steady state solution of an equation of motion
to be able to sketch the frequency response curve

key ideas and/or vocabulary

periodic, forcing term

transient term in solution
steady state solution

frequency gain

resonance curve

resonance frequency

system at resonance

solved problems - using key ideas

sketching a frequency curve, #1

determining the equation of motion for an undamped system at resonance, #4

calculating the displacement of a forced overdamped system, #8

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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