# HW4_10 - (x). The string is fixed at one end and has a...

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ME 563 HOMEWORK # 4 Fall 2010 PROBLEM 1: (35%) Derive the unforced equations of motion for the continuous vibrating rod below with cross sectional area, A(x) , modulus of elasticity, E , and density, ρ (x). The rod is free to vibrate at both ends (HINT: P(x)=EA(x) ε =EA(x) u/ x ). PROBLEM 2: (35%) Derive the unforced equations of motion for the continuous vibrating string below with tension, T(x) , and linear density,
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Unformatted text preview: (x). The string is fixed at one end and has a concentrated mass at its other end. Ignore forces due to gravity. PROBLEM 3 (30%) Use ten lumped masses, M i , to model the continuous vibrating system in PROBLEM 1 above with uniform cross sectional area, A . Compare your results with those from PROBLEM 1. Explain why, when, and how the two results are similar....
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## This document was uploaded on 12/23/2011.

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