Differential equation - deflection of bar.

**johnsy123** · August 15th 2011, 10:51 PM

I am having trouble obtaining the answer of the following problem:

The deflection of a 5-meter-long board from the horizontal satisfies the differential equation d^2y/dx^2=-0.0004(5-x)^2, where x is the horizontal distance from its fixed end. If the deflection is zero and the board is horizontal at its fixed end, then find:
a)the equation which measures the deflection at any point

**Prove It** · August 16th 2011, 03:00 AM

Originally Posted by johnsy123

I am having trouble obtaining the answer of the following problem:

The deflection of a 5-meter-long board from the horizontal satisfies the differential equation d^2y/dx^2=-0.0004(5-x)^2, where x is the horizontal distance from its fixed end. If the deflection is zero and the board is horizontal at its fixed end, then find:
a)the equation which measures the deflection at any point

Assuming that $\displaystyle y$ represents the deflection, then

$\displaystyle \begin{align*} \frac{d^2y}{dx^2} &= -0.0004(5-x)^2 \\ \frac{d^2y}{dx^2} &= -0.0004(25 - 10x + x^2) \\ \frac{d^2y}{dx^2} &= -0.01 + 0.004x - 0.0004x^2 \\ \frac{dy}{dx} &= \int{-0.01 + 0.004x - 0.0004x^2\,dx} \\ \frac{dy}{dx} &= -0.01x + 0.002x^2 - \frac{0.0004}{3}x^3 + C_1\end{align*}$

Keep going to find $\displaystyle y$ and use your conditions to evaluate the constants.

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