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 3 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) = mAow² sin wt on the second floor. Complete parts (a) and (b). (a) What is the natural frequency (in hertz) of oscillations of the second floor? @o (Type an exact answer, using radicals as needed.)

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 3 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) = mAow² sin wt on the second floor. Complete parts (a) and (b). (a) What is the natural frequency (in hertz) of oscillations of the second floor? @o (Type an exact answer, using radicals as needed.)