The vibrations of a bridge obey the following differential equation:u′′+ 36u= 3 sin(2w0t) + 4 cos(w20t),where 3 sin(2w0t) + 4 cos(w20t) are the forced vibrations caused by the wind and the waves. Find the value(s) of w0 for which the bridge is likely to collapse due to the resonance.

For resonance the excitation of large oscillation ehen input frequency and natural frequency is…

Answered: The vibrations of a bridge obey the…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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The vibrations of a bridge obey the following differential equation:

u′′+ 36u= 3 sin(2w₀t) + 4 cos(w²₀t),where 3 sin(2w₀t) + 4 cos(w²₀t) are the forced vibrations caused by the wind and the waves. Find the value(s) of w₀for which the bridge is likely to collapse due to the resonance.

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