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A particular spring has a spring constant of 50 Newton/meters. Suppose a 1/2 kg mass is...

A particular spring has a spring constant of 50 Newton/meters. Suppose a 1/2 kg mass is hung on the spring and is initially sent in motion with an upward velocity of 10 meters per second, 1/2 meter below the equilibrium position.

A) Write down the DE that models the motion of this spring.

B) Write down the initial conditions.

C) Find the equation of motion for the spring.

D) Suppose this spring mass system experiences a viscous damping term that is 6 times the instantaneous velocity. Write the DE that would model this system. DO NOT SOLVE THE DE.

E) Without solving the DE you wrote in part D, would this result in under, over, or critical damping? Show your work in determining this.

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