Consider a model of a building whose base moves as a result of an earthquake. The building can be modeled as a single-degree-of-freedom spring-mass system where the building mass is lumped on top of two beams used to model the walls of the building. The ground motion has an amplitude of 0.1 m and a frequency of 7.5 rad/s. The building mass is 105 kg and the stiffness in bending of each wall is 3.519*10^6N/m.
a) Write down the equation of motion of the mass, which represents the building.
b) Compute the natural frequency
c) Compute the amplitude X of the steady-state response.
d) Does the amplitude seem large? Comment on your answer.
e) What is the amplitude of the force transmitted to the building?