# hw1 - it deep into the ground After each hit the weight is...

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ME 375 HOMEWORK #1 Spring 2009 Out: Jan. 14, 2009 Due: Jan. 21, 2009 Problem 1 : (30%) For each of the following systems, draw a schematic model representation using lumped mass, spring, and damping elements. Label each of the elements in your model. State any assumptions that you make. Make sure you include any pertinent inputs. a) A loaded elevator as it moves from floor to floor b) An accelerometer mounted on a vibrating structure c) A tow truck pulling in a car stranded in the ditch Problem 2 : (35%) Pile drivers are used to drive piles that serve as foundations for modern high-rise buildings. A weight having mass m is dropped from a height h onto the top of the pile (with mass M) to push
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Unformatted text preview: it deep into the ground. After each hit, the weight is lifted up and dropped again, until the pile is securely planted in the ground. Assume that the ground can be represented by a viscous damper with damping coefficient b. Also assume that h remains the same for each hit. a) Draw a schematic of the system using basic modeling elements. Treat the weight as being stuck on top of the pile for each driving stroke. b) Draw FBDs for each basic element. c) Derive the equations of motion. d) Determine initial conditions for the combined masses just as the weight hits the top of the pile the first time. Problem 3 : (35%) Problem B-3-14 (p. 103 of Ogata text)...
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