Second Order ODE (damping effect) will rate lifesaver

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Help me finish. Image text transcribed for accessibility: A mass M = 5 kg is connected to a spring-dashpot system with spring constant k = 100N/m and a damper with coefficient c = 20N s/m. Assume that the acceleration of gravity is g = 10m/s. Determine if the system is un-damped, under-damped, critically damped, or over-damped and find the equation of motion y(t) if y(0) = 0 and y'(0) = 0. M= 5 kg K = 100 N/m C = 20 N s/m g = 10 mk

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