i) A uniform rigid shelf is supported on symmetrically placed identical elastic supports as shown in Figure 3.1. The shelf is of length 2L, mass m and moment of inertia about its centre Im. The supports have stiffness k and are positioned equally spaced apart a distance 2a about the centre of mass C. Centre of mass C k 2a 0 2L Figure 3.1. A shelf on its elastic supports Determine the two lowest natural frequencies, where the shelf is considered to be rigid and undergoing small rotation , about C, and displacement y, of C, from the horizontal equilibrium position. a) Derive the equations of motions, using Lagrange's equations, in terms of the rotation and the displacement. Clearly state any assumptions made and show the relevant diagrams or relationships used in the derivation.

i) A uniform rigid shelf is supported on symmetrically placed identical elastic supports as shown in Figure 3.1. The shelf is of length 2L, mass m and moment of inertia about its centre Im. The supports have stiffness k and are positioned equally spaced apart a distance 2a about the centre of mass C. Centre of mass C k 2a 0 2L Figure 3.1. A shelf on its elastic supports Determine the two lowest natural frequencies, where the shelf is considered to be rigid and undergoing small rotation , about C, and displacement y, of C, from the horizontal equilibrium position. a) Derive the equations of motions, using Lagrange's equations, in terms of the rotation and the displacement. Clearly state any assumptions made and show the relevant diagrams or relationships used in the derivation.

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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