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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