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Derive the differential eq, governing the motion of the system, use x as the generalizing co-ordinate, assume small x and determine the natural frequency of the system.
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KE=(KE)rod+(KE)M

=12 IG˙θ2 + 12 M (˙x)2

=12[mL212] [2˙xL]2 + 12 M˙x2

=12 [m3+M]˙x2

PE = 12 k (x)2

Keq = K

W.D. =  cy dy

y=L2 θ=x

˙y=L2 ˙θ=˙x

=  c˙x dx

Ceq = C

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