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Unformatted text preview: Differential Equations Test 3 Solutions Answer FOUR questions. Show all working clearly. 1. Given that y 1 = x and y 2 = 1 /x are solutions of the homogeneous equation x 2 y 00 + xy- y = 0 find a paricular solution of the differential equation x 2 y 00 + xy- y = x. 2. A particle of mass 1kg is attached to a horizontally-mounted spring of stiffness 25N/m. The mass is moved 20cm to the right and given an initial speed of 1m/s to the right; calculate the maximum displacement of the mass from equilibrium. 3. A mass hangs from a vertically-mounted spring and in so doing stretches the spring by a distance l . Show that when the mass is displaced vertically from its rest position, the resulting oscillations have period 2 p l/g . 4. A free mechanical vibration is described by the equation m x + b x + kx = 0 . (i) When is the vibration: undamped? underdamped? critically damped? overdamped?...
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This note was uploaded on 11/12/2011 for the course MAP 2302 taught by Professor Tuncer during the Fall '08 term at University of Florida.
- Fall '08