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Homework 4

# Homework 4 - ME 391 Homework 4 Assigned Due Mar 7 2008...

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Unformatted text preview: ME 391 Homework 4 Assigned: Feb 27, 2008 Due: Mar 7, 2008 Problem 1: Using the Variation of Parameters, solve: y” — y’ — 2y = e 3" (5 pts) Problem 2: A 20-kg mass is attached to a spring. If the frequency of the simple harmonic motion is 2 / 7r cycles/s, what is the spring constant k? What is the frequency of simple harmonic motion if the original mass is replaced with an 80-kg mass? (5 pts) Problem 3: A mass of % slug is attached to a spring having a spring constant of 1 lb/ft. The mass is started in motion by initially displacing it 2 ft. in the downward direction and giving it an initial velocity of 2 ft/sec in the upward direction. Find the equation of motion of the mass, if the force due to air resistance is -1xlb. (5 pts) Problem 4: A 10-kg mass is attached to a spring having a spring constant of 140 N/m. The mass is started in motion from the equilibrium position with an initial velocity of 1 m/sec in the upward direction and with an applied external force F (t) = 5 sin t. Find the equation of motion of the mass if the force due to air resistance is -90xN. (5 PtS) Problem 5: An RCL circuit connected in series has R = 10 ohms, C = 10‘2 farad, L = 1/z henry, and an applied voltage E = 12 volts. Assuming no initial charge at t = 0 when the voltage is ﬁrst applied, ﬁnd the subsequent equation for the current in the system. (10 pts) ...
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