Consider a thin rod having mass \(m\) and of length \(l\) pivoted at one of its end. It is held by a spring at its midpoint and another at its far end, both pulling in opposite directions. The springs have spring constant \(k\), and at equilibrium their pull is perpendicular to the rod. If (for small oscillations)- \[ \omega^2 = \frac{ak}{bm} - \frac{cg}{dl} \]

Find \[\frac{a+c}{b+d}\]

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