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 A0 and circular frequency ω, resulting in an external horizontal force
$F(t) = m A_0 \omega^2 \sin(\omega t)$
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 2.25s with an amplitude of 3 in, what is the amplitude of the resulting forced oscillations of the second floor?
Above is the full textbook question. I'm having difficulty fully understanding what the second part of the problem entails. Here's what I've done so far:
$m = 1000 [slugs]$
$F_g = 32000 [lbs]$
$F_k = kx$
$F(t) = mA_0\omega^2\sin(\omega t)$
$\omega_0 = \sqrt(k/m) = \sqrt(10000/1000) = \sqrt10$; answers part a
$mx'' + kx = F(t), c = 0$
$F_0 = A_0\omega^2$
$\omega = 1 (cycle)/(2.25 [s])$
$A_0 = 3 [in]$