The vibrations of a bridge obey the following differential equation: u′′+ 36u= 3 sin(2w 0 t) + 4 cos(w 2 0 t),where 3 sin(2w 0 t) + 4 cos(w 2 0 t) are the forced vibrations caused by the wind and the...

The vibrations of a bridge obey the following differential equation:

u′′+ 36u= 3 sin(2w₀t) + 4 cos(w²
₀t),where 3 sin(2w₀t) + 4 cos(w²
₀t) 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.