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The fall 2011 test ii for the egr 265 course, math tools for engineering problem solving. The test consists of six problems covering various topics in engineering mathematics, including solving differential equations and analyzing spring-mass systems.
Typology: Exams
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Problem 1 (20 points)
Solve the initial value problem
y′′^ + 2y′^ + 10y = 0, y(0) = 1, y′(0) = 2.
Problem 2 (20 points)
Find the general solution of y′′^ − 4 y′^ + 4y = 5x.
Problem 4 (10 points)
Find the general solution of y′′′^ + 2y′′^ + y′^ = 0.
Problem 5 (20 points)
A 64 pound weight stretches an undamped spring by 8 feet. (a) Working in English units, find the value of the spring constant k in lb/ft and the mass m of the weight in slugs. (b) Find the equation of motion of the undamped spring-mass system. (c) Find the equation of motion if the mass is released at a position of 1 feet above the equilibrium at a downward velocity of 1ft/s. Assume here that the positive x-direction is oriented downwards.
