1) A building consists of two floors. The first floor is attached rigidly to the ground, and the second floor is of mass m = 1000 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 5 tons to displace the second floor a distance of 1 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) = mA¸w²sin(wt) on the second floor. a. What is the natural frequency (in hertz) of oscillations of the second floor? b. If the ground undergoes one oscillation every 2.25 s with an amplitude of 3 in, what is the amplitude of the resulting forced oscillations of the second floor?
1) A building consists of two floors. The first floor is attached rigidly to the ground, and the second floor is of mass m = 1000 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 5 tons to displace the second floor a distance of 1 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) = mA¸w²sin(wt) on the second floor. a. What is the natural frequency (in hertz) of oscillations of the second floor? b. If the ground undergoes one oscillation every 2.25 s with an amplitude of 3 in, what is the amplitude of the resulting forced oscillations of the second floor?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:1) A building consists of two floors. The first floor is attached rigidly to the ground, and the second
floor is of mass m = 1000 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 5 tons to displace the second floor a distance of 1 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) = mA¸w²sin(wt) on the second floor.
a. What is the natural frequency (in hertz) of oscillations of the second floor?
b. If the ground undergoes one oscillation every 2.25 s with an amplitude of 3 in, what is the
amplitude of the resulting forced oscillations of the second floor?
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