GATE Civil Engineering
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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

$$\frac{d^2y}{dx^2}+\frac{P}{EI}y=0$$

If $a$ is amplitude constant for $y,$ then

  1. $y=\dfrac{1}{P} \bigg( 1- a \cos \dfrac{2 \pi x}{L} \bigg) \\$
  2. $y=\dfrac{1}{P} \bigg( 1- a \sin \dfrac{2 \pi x}{L} \bigg) \\$
  3. $y= a \sin \dfrac{n \pi x}{L} \\$
  4. $y= a \cos \dfrac{n \pi x}{L}$
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