(a) Derive, in detail, the crucial formula (16). (b) By considering dC/dc show that C (? max...

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(a) Derive, in detail, the crucial formula (16).

(b) By considering dC*/dc show that C* (?_max) increase as c ( ?2mk) decreases.

(c) Illustrate practical resonance with an ODE of your own in which you vary c, and sketch or graph corresponding curves as in Fig. 57.

(d) Take your ODE with c fixed and an input of two terms, one with frequency close to the practical resonance frequency and the other not. Discuss and sketch or graph the output.

(e) Give other applications (not in the book) in which resonance is important.

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Advanced Engineering Mathematics

ISBN: 978-0470458365

10th edition

Authors: Erwin Kreyszig

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Question Posted: Jun 14, 2022 05:00 AM

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(a) Derive, in detail, the crucial formula (16). (b) By considering dC*/dc show that C* (? max...

Question:

3 2 1 T |C= 08 0 1 1 200 Fig. 57. Amplification C*/Fo as a function of w for m = 1, k = 1, and various values of the damping constant c

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a The crucial formula 16 is derived from the mathematical expression of the oscillator equation which is given by md2xdt2 cdxdt kx Ft The solution to ...View the full answer

Advanced Engineering Mathematics

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