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ωn1 = [ (1/2) ( k1 / m1 + k2 / m2 ( 1 + m2/m1 ) + ( ( k1/m1 + k2/m2 ( 1 + m2/m1) )2 - ( 4 k1k2 / ( m1m2)1/2 ]1/2
ωn2 = [ (1/2) ( k1 / m1 + k2 / m2 ( 1 + m2/m1 ) - ( ( k1/m1 + k2/m2 ( 1 + m2/m1) )2 - ( 4 k1k2 / ( (m1m2)1/2 ]1/2

Where:

k1,2 = Spring Stiffness (lb/in)
m1,2 = Mass ( lb-sec2 / in )
ωn1, n2 = Angular Natural Frequency (rad/sec)

Reference Harris, Shock and Vibration Handbook

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