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If the following equation establishes equilibrium in slightly bent position, the mid-span deflection of a member shown in the figure is (d² y)/(dx²) + (P)/(EI) y = 0 If a is amplitude constant for y, then

1. y = (1)/(P) (1 - acos (2π x)/(L))
2. y = (1)/(P) (1 - asin (2π x)/(L))
3. y = asin (π x)/(L)
4. y = acos (π x)/(L)

Correct answer: y = asin (π x)/(L)

Solution

The correct option describes a sinusoidal function, which is characteristic of the deflection shape of a beam under uniform loading conditions, satisfying the second-order differential equation given. This form accurately represents the boundary conditions and the nature of the bending in the member.

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