Question

7. Tow pendulums are connected using a spring as shown. (a) Derive the equation of motion using Lagrange's equation. (b) Using Modal analysis derive the Characteristic equation, and natural frequencies. (c) Using Eigenvector, draw mode shapes (indicate the directions). (d) Derive the equation of motion in modal coordinates.

          7. Tow pendulums are connected using a spring as shown.
(a) Derive the equation of motion using Lagrange's equation.
(b) Using Modal analysis derive the Characteristic equation, and natural
frequencies.
(c) Using Eigenvector, draw mode shapes (indicate the
directions).
(d) Derive the equation of motion in modal coordinates.

7. Tow pendulums are connected using a spring as shown.
(a) Derive the equation of motion using Lagrange's equation.
(b) Using Modal analysis derive the Characteristic equation, and natural
frequencies.
(c) Using Eigenvector, draw mode shapes (indicate the
directions).
(d) Derive the equation of motion in modal coordinates.

Added by Robert S.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Madhur L

08/14/2023

Step 1

Let's denote the angles of the two pendulums as θ1 and θ2, and let x be the displacement of the spring from its equilibrium position. The generalized coordinates are then q1 = θ1, q2 = θ2, and q3 = x. The Lagrangian is given by the difference between the kinetic Show more…

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Two pendulums are connected using a spring as shown. (a) Derive the equation of motion using Lagrange's equation. (b) Using Modal analysis, derive the Characteristic equation and natural frequencies. (c) Using Eigenvectors, draw mode shapes and indicate the directions. (d) Derive the equation of motion in modal coordinates. F = f*sin(t) k m 3m