Consider a mechanical system consisting of two metal plates and two springs, connected vertically as shown in Figure 2. Let m₁, m2 repre- sent the masses of the metal plates, 91, 92 represent their positions, and l1.l2 represent the natural lengths of the springs. Suppose the spring forces are nonlinear functions of the actual lengths of the springs, given by F1 (31) = k₁(y1 - ₁)³ and F2(y2 - y1) = k2(y2 - Y1 - 2)³, respectively. Let g denote the gravitational constant. (a) Using Newton's second law, derive the equations of motion gov- erning the system (i.e., differential equations in ÿ₁ and 2). (b) Let Yel Ye2 represent the equilibrium point of the system, i.e., the positions y₁, y2 when the system is at rest. Determine Yel, Ye2 by setting ₁ = 2 = 0 and express yel, Ye2 as functions of mi, m2, l1, l2, k1, k2, g. YI Y2 www. mi Gravity m₂ Figure 2

Consider a mechanical system consisting of two metal plates and two springs, connected vertically as shown in Figure 2. Let m₁, m2 repre- sent the masses of the metal plates, 91, 92 represent their positions, and l1.l2 represent the natural lengths of the springs. Suppose the spring forces are nonlinear functions of the actual lengths of the springs, given by F1 (31) = k₁(y1 - ₁)³ and F2(y2 - y1) = k2(y2 - Y1 - 2)³, respectively. Let g denote the gravitational constant. (a) Using Newton's second law, derive the equations of motion gov- erning the system (i.e., differential equations in ÿ₁ and 2). (b) Let Yel Ye2 represent the equilibrium point of the system, i.e., the positions y₁, y2 when the system is at rest. Determine Yel, Ye2 by setting ₁ = 2 = 0 and express yel, Ye2 as functions of mi, m2, l1, l2, k1, k2, g. YI Y2 www. mi Gravity m₂ Figure 2

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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