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.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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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 w0 for which the bridge is likely to collapse due to the resonance.

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