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Chapter 46, Problem 2RQ

Explain the difference between sprung and unsprung weight.

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An aluminum rod of length L = 1m has mass density p = 2700 kg and Young's modulus E = 70 GPa. The rod is fixed at both ends. The exact natural eigenfrequencies of the rod are wexact E = √ ρ for n=1,2,3,. . . . 1. What is the minimum number of linear elements necessary to determine the fundamental frequency w₁ of the system? Discretize the rod in that many elements of equal length, assemble the global system of equations KU = w² MU, and find the fundamental frequency w₁. Compute the relative error e₁ = (w1 - wexact) /w exact Sketch the fundamental mode of vibration. 2. Use COMSOL to solve the same problem. Show the steps necessary to find the fundamental frequency and mode of the rod. What is the relative error using linear elements and a normal mesh?
A ball with a mass of 5.0 kg is hanging from a string and is initially at rest. A bullet with a mass of 10.0 g and a velocity of 200.0 m/s is fired at the ball. The bullet embeds itself inside the ball. How high (h) do the ball and the bullet rise? Gravitational acceleration: g=9.81g = 9.81g=9.81 m/s².
Don't use chatgpt. Need handwritten solution. Mechanical engineering

Chapter 46 Solutions

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