The respective expressions for complimentary function and particular integral part of the solution of the differential equation $\frac{d^{4} y}{d x^{4}}+3 \frac{d^{2} y}{d x^{2}}=108 x^{2}$ are

(A) $\left\lfloor c_{1}+c_{2} x+c_{3} \sin \sqrt{3} x+c_{4} \cos \sqrt{3} x\right\rfloor$ and $\left[3 x^{4}-12 x^{2}+c\right]$

(B) $\left\lfloor c_{2} x+c_{3} \sin \sqrt{3} x+c_{4} \cos \sqrt{3} x\right]$ and $\left[5 x^{4}-12 x^{2}+c\right]$

(C) $\left.\mid c_{1}+c_{3} \sin \sqrt{3} x+c_{4} \cos \sqrt{3} x\right\rfloor$ and $\left[3 x^{4}-12 x^{2}+c\right]$

(D) $\left\lfloor c_{1}+c_{2} x+c_{3} \sin \sqrt{3} x+c_{4} \cos \sqrt{3} x\right\rfloor$ and $\left[5 x^{4}-12 x^{2}+c\right]$

The respective expressions for complimentary function and particular integral part of the solution of the differential equation $\frac{d^{4} y}{d x^{4}}+3 \frac{d^{2} y}{d x^{2}}=108 x^{2}$ are

(A) $\left\lfloor c_{1}+c_{2} x+c_{3} \sin \sqrt{3} x+c_{4} \cos \sqrt{3} x\right\rfloor$ and $\left[3 x^{4}-12 x^{2}+c\right]$

(B) $\left\lfloor c_{2} x+c_{3} \sin \sqrt{3} x+c_{4} \cos \sqrt{3} x\right]$ and $\left[5 x^{4}-12 x^{2}+c\right]$

(C) $\left.\mid c_{1}+c_{3} \sin \sqrt{3} x+c_{4} \cos \sqrt{3} x\right\rfloor$ and $\left[3 x^{4}-12 x^{2}+c\right]$

(D) $\left\lfloor c_{1}+c_{2} x+c_{3} \sin \sqrt{3} x+c_{4} \cos \sqrt{3} x\right\rfloor$ and $\left[5 x^{4}-12 x^{2}+c\right]$

1 Answer

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$\left\lfloor c_{1}+c_{2} x+c_{3} \sin \sqrt{3} x+c_{4} \cos \sqrt{3} x\right\rfloor$ and $\left[3 x^{4}-12 x^{2}+c\right]$

A $3 \mathrm{~m}$ long simply supported beam of uniform cross section is subjected to a uniformly distributed load of $\mathrm{w}=20 \mathrm{kN} / \mathrm{m}$ in the central $1 \mathrm{~m}$ as shown in the figure.

If the flexural rigidity (EI) of the beam is $30 \times 10^{6} \mathrm{~N}-\mathrm{m}^{2}$, the maximum slope (expressed in radians) of the deformed beam is

(A) $0.681 \times 10^{-7}$

(B) $0.943 \times 10^{-7}$

(C) $4.310 \times 10^{-7}$

(D) $5.910 \times 10^{-7}$

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