[3 pts] 14 pts) S Problem 2 By using text and drawings, provide short but complete...

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[3 pts] 14 pts) S Problem 2 By using text and drawings, provide short but complete answer to the following: Your technician brought you nodal patterns of a solid circular plate which was excited by an actuator placed at the plate's center. Over a frequency range up to 10 kHz, the technician observed a variety of nodal patterns (formed by sand grains) which corresponded to various of nodal circles. However, modes having non-zero number of nodal diameters were not observed. The technician was confused because nodal diameters were never observed in the measurements. From physical and mathematical standpoints, please give a detailed explanation why. [5 pts] A young engineer has just completed a course in dynamics and has learned two things. First, the tension/compression wave propagation speed in an elastic rod is c = E/p. Second, Newton's law states that the acceleration of the mass center equals the resultant external force divided by the body's total mass. One day, the young engineer and his/her friend, an old engineer, were discussing the vibration of a uniform clastic rod of length L that rests on a smooth horizontal surface. At =0, the left end of the rod is hit with a hammer. A young engineer said "It will take a small but finite time for the compression wave to travel from the end of the rod, and so the mass center won't move until 1-L/2c." The old engineer said "I disagree. The mass center of the rod will move immediately, at 1-0, in accordance with Newton's law." At which point the young engineer replied "Since nothing, including elastic waves, can travel faster than the speed of light, the mass center can't move at 0" Do you agree with the young engineer or old engineer? State in detail your reasons, and address the following question: because of finite wave speeds, does Newton's law remain valid for an entire elastic [5 pts] body? [3 pts] 14 pts) S Problem 2 By using text and drawings, provide short but complete answer to the following: Your technician brought you nodal patterns of a solid circular plate which was excited by an actuator placed at the plate's center. Over a frequency range up to 10 kHz, the technician observed a variety of nodal patterns (formed by sand grains) which corresponded to various of nodal circles. However, modes having non-zero number of nodal diameters were not observed. The technician was confused because nodal diameters were never observed in the measurements. From physical and mathematical standpoints, please give a detailed explanation why. [5 pts] A young engineer has just completed a course in dynamics and has learned two things. First, the tension/compression wave propagation speed in an elastic rod is c = E/p. Second, Newton's law states that the acceleration of the mass center equals the resultant external force divided by the body's total mass. One day, the young engineer and his/her friend, an old engineer, were discussing the vibration of a uniform clastic rod of length L that rests on a smooth horizontal surface. At =0, the left end of the rod is hit with a hammer. A young engineer said "It will take a small but finite time for the compression wave to travel from the end of the rod, and so the mass center won't move until 1-L/2c." The old engineer said "I disagree. The mass center of the rod will move immediately, at 1-0, in accordance with Newton's law." At which point the young engineer replied "Since nothing, including elastic waves, can travel faster than the speed of light, the mass center can't move at 0" Do you agree with the young engineer or old engineer? State in detail your reasons, and address the following question: because of finite wave speeds, does Newton's law remain valid for an entire elastic [5 pts] body?