Stepping voltages down to lower values is a common design challenge. A straight-forward solution to this is a voltage divider such as the circuit below. This designsynthesis has one degree-of-freedom. A measure (metric) of the effectiveness of the designis the efficiency of the circuit, defined as

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?