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Fall 2017 Math 2150 Final Exam Take 1 Part 2 Section 8 Closed book, closed notes. No caleulators. Show your work. No loitering, no smoking, no walking on the grass, no feeding the animals, no parking, no stopping or standing, no dumping, no running, no fishing, no vacancy. All problems weighted equally. (1) Use the power series method to solve (1-z)y" +zy-y = 0. Here's a standard power series that you will find useful in your answer: 23 2 3 4! n! nao (2) A 64 Ib object stretches a spring 4 ft in equilibrium. It is attached to a dashpot with damping constant c-8 lb-sec/ft. The object is initially displaced 18 inches above equilibrium and given a downward velocity of 4 ft/sec. Find its displacement for t>0. Assume the motion is free. Since the weight is 64, for the mass you can use m =64/32 = 2. The following equations will be useful: The equation of motion for this system is my" + c/ + ky= F, where m is the mass of the object, c is the damping constant, k is the spring constant, and F is the forcing function. mg = kar, where g 32n/s2 is the gravitational constant, and Al is the distance by which a spring is stretched from its natural length when the object is attached to it. Remember to convert from inches to feet, so all units are compatible.
