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The system illustrated in Figure Q3 shows a mechanism of mass 3m that can slide horizontally and with its displacement given by x. This mass restrained by a spring of stiffness 2k, with the other end of the spring attached to a solid unmoveable surface. The mass is connected to a lever, or bar, of mass m and length 6L, by a spring of stiffness k. The lever pivots about its centre, and the angular motion is restricted by a spring of stiffness 4k attached to the other end of the lever. Assuming small angular displacements of the lever, 6, show that the equations of motion for this system are given by: mä + kx – kL0 = 0 mLÖ + 15kL0 – kx = 0

The system illustrated in Figure Q3 shows a mechanism of mass 3m that can slide horizontally and with its displacement given by x. This mass restrained by a spring of stiffness 2k, with the other end of the spring attached to a solid unmoveable surface. The mass is connected to a lever, or bar, of mass m and length 6L, by a spring of stiffness k. The lever pivots about its centre, and the angular motion is restricted by a spring of stiffness 4k attached to the other end of the lever. Assuming small angular displacements of the lever, 6, show that the equations of motion for this system are given by: mä + kx – kL0 = 0 mLÖ + 15kL0 – kx = 0

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Q3 The system illustrated in Figure Q3 shows a mechanism of mass 3m that can slide horizontally and with its displacement given by x. This mass restrained by a spring of stiffness 2k, with the other end of the spring attached to a solid unmoveable surface. The mass is connected to a lever, or bar, of mass m and length 6L, by a spring of stiffness k. The lever pivots about its centre, and the angular motion is restricted by a spring of stiffness 4k attached to the other end of the lever. (a) Assuming small angular displacements of the lever, 0, show that the equations of motion for this system are given by: mä + kx – kL0 = 0 mLÖ + 15kLO – kx = 0 (b) Calculate the natural frequencies of the system given the following properties: m = 5 kg; L= 0.5 m; k= 1200 N/m 4k 3L 3L 2k Figure Q3
Transcribed Image Text:Q3 The system illustrated in Figure Q3 shows a mechanism of mass 3m that can slide horizontally and with its displacement given by x. This mass restrained by a spring of stiffness 2k, with the other end of the spring attached to a solid unmoveable surface. The mass is connected to a lever, or bar, of mass m and length 6L, by a spring of stiffness k. The lever pivots about its centre, and the angular motion is restricted by a spring of stiffness 4k attached to the other end of the lever. (a) Assuming small angular displacements of the lever, 0, show that the equations of motion for this system are given by: mä + kx – kL0 = 0 mLÖ + 15kLO – kx = 0 (b) Calculate the natural frequencies of the system given the following properties: m = 5 kg; L= 0.5 m; k= 1200 N/m 4k 3L 3L 2k Figure Q3
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