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M = k√(L₁L₂)
M= 0.45√(100*900)
M = 135 mH
L_eq for opposite connection of coils = L₁ + L₂ - 2M
L_eq = 900 + 100 - 2*135
L_eq = 730 mH
Frequency of natural oscillation is given by,
fn = {((dPe/dδ)at(δo))/M)}
dPe/dδ = ((V1*V2)/X*(cosδ))
= (11/05)*cosδ
= (11/0.5)*0.5
M = (H*s)/(πf)
= 4/(50π)
fn = (1.76*(3/50π))
= 9.4 rad/sec = 1.32 Hz