A 2 kg mass is hung from a spring with spring constant 10 N/m. The overall shape and size of the object gives a drag coefficient of 11 Ns/m. The object is allowed to hang at rest on the spring, and is then dragged downward 0.8 m and pushed upward with a velocity of 1.5 m/s as it is released. Write an initial value problem describing the motion of this mass as a function of time. You do NOT need to solve this initial value problem, just write it completely. Is this physical system undamped, underdamped, critically damped, or overdamped? Explain your reasoning. Pick one of the parameters in this problem and change it to make the physical system critically damped. Your answer should include the part of the problem statement that you are changing, what you are changing it to, and how you know this makes the physical system critically damped.

A 2 kg mass is hung from a spring with spring constant 10 N/m. The overall shape and size of the object gives a drag coefficient of 11 Ns/m. The object is allowed to hang at rest on the spring, and is then dragged downward 0.8 m and pushed upward with a velocity of 1.5 m/s as it is released. Write an initial value problem describing the motion of this mass as a function of time. You do NOT need to solve this initial value problem, just write it completely. Is this physical system undamped, underdamped, critically damped, or overdamped? Explain your reasoning. Pick one of the parameters in this problem and change it to make the physical system critically damped. Your answer should include the part of the problem statement that you are changing, what you are changing it to, and how you know this makes the physical system critically damped.

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