The New England Merchants Bank Building in Boston is 152 m high. On windy days it sways with a frequency of 0.15Hz , and the acceleration of the top of the building can reach 2.5% of the free-fall acceleration, enough to cause discomfort for occupants.
What is the total distance, side to side, that the top of the building moves during such an oscillation?

Suppose that a mass of 2 kg is attached a spring whose spring constant is 50. the system is damped such that b = 12 . the mass is set in motion with an initial velocity of -8 m/s at a position 0 meters from equilibrium. set up and solve a differential equation that models this motion. write your solution in the form a cos ( ω t − α ) where α is a positive number. use your solution to fill in the information below: what is the amplitude of the motion? what is the value of ω ? what is the phase shift?