Aperegrine falcon dives at a pigeon. the falcon starts downward from rest and falls with free-fall acceleration. if the pigeon is 75.6 m below the initial position of the falcon, how long does the falcon take to reach the pigeon? assume that the pigeon remains at rest. the acceleration of gravity is 9.8 m/s 2 . answer in units of s.

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?