(b) If the ground undergoes one oscillation every 4.25 s with an amplitude of 11 in., what is the amplitude of the resulting forced oscillations of the second floor?

Principles of Physics: A Calculus-Based Text
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Author:Raymond A. Serway, John W. Jewett
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Chapter12: Oscillatory Motion
Section: Chapter Questions
Problem 11OQ
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A building consists of two floors. The first floor is attached rigidly to the ground, and the second floor is of mass
m = 1,000 slugs (fps units) and weighs 16 tons (32,000 lb). The elastic frame of the building behaves as a spring that
resists horizontal displacements of the second floor; it requires a horizontal force of 10 tons to displace the second
floor a distance of 2 ft. Assume that in an earthquake the ground oscillates horizontally with amplitude A and circular
frequency w, resulting in an external horizontal force F(t) = mAow² sin oot on the second floor. Complete parts (a)
and (b).
(a) What is the natural frequency (in hertz) of oscillations of the second floor?
wo = √10 (Type an exact answer, using radicals as needed.)
(b) If the ground undergoes one oscillation every 4.25 s with an amplitude of 11 in., what is the amplitude of the
resulting forced oscillations of the second floor?
a = inches (Type an integer or decimal rounded to three decimal places as needed.)
Transcribed Image Text:A building consists of two floors. The first floor is attached rigidly to the ground, and the second floor is of mass m = 1,000 slugs (fps units) and weighs 16 tons (32,000 lb). The elastic frame of the building behaves as a spring that resists horizontal displacements of the second floor; it requires a horizontal force of 10 tons to displace the second floor a distance of 2 ft. Assume that in an earthquake the ground oscillates horizontally with amplitude A and circular frequency w, resulting in an external horizontal force F(t) = mAow² sin oot on the second floor. Complete parts (a) and (b). (a) What is the natural frequency (in hertz) of oscillations of the second floor? wo = √10 (Type an exact answer, using radicals as needed.) (b) If the ground undergoes one oscillation every 4.25 s with an amplitude of 11 in., what is the amplitude of the resulting forced oscillations of the second floor? a = inches (Type an integer or decimal rounded to three decimal places as needed.)
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