8. A mass of 1 kg is attached to a spring hanging vertically from the ceiling. Suppose the damping coefficient o equals 2 kg/s. And the spring constant k equals 5 kg-s2. a. Is the spring-mass system overdamped, underdamped, or critically damped? b. If left hanging, the mass causes the spring to stretch by AL due to gravity beyond its natural spring length. Find AL. Assume that the acceleration due to gravity is g = 10 m/s. / c. The mass is lifted up to the position where spring is neither stretched or compressed. (Think about how far above the equilibrium position this is using your answer from part b.) Then, the mass is simply let go so that it has an initial velocity of 0 m/s. Find the expression for its position as a function of time, i.e., x(t). / Use a vertical coordinate system where x 0 is the equilibrium length of the spring that's stretched by AL due to gravity and x is positive downwards (corresponding to stretching the spring).

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In the mid-20th century, the availability and the growth in power of digital computers led to the increase in the mathematical model in the field of engineering and science. The analysis of these detailed models needs to be increased.