Consider a shaft

*AB*fixed at both ends and carrying a uniformly distributed load '*w'*per unit length as shown in Fig.,
We know that the static deflection at a distance '

*x'*from A is given by
Integrating the above equation on both sides with limits from 0 to l,

Now integrating

*y*^{2}within the limits from 0 to l,
We know that

and natural frequency,

Since the static deflection of a shaft fixed at both ends and carrying a uniformly distributed load is

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