WeBWorK Standalone Renderer

Suppose a uniform beam of length $3$ is simply supported at $x = 0$ and $x = 3$ . If the load per unit length of the beam is given by w(x), $0<x<3$ , then the differential equation modeling the deflection of the beam y(x) is given by $EI \frac{d^4 y}{dx^4} = w(x)$ Because the beam is simply supported at both ends we know that $y(x) = \displaystyle\sum\limits_{n=0}^\infty b_n \sin\!\left(\frac{n\pi x}{3}\right)$ and using a Fourier Sine series expansion on $[0,3]$ we get

$b_n$

$=$

$\displaystyle\int$

$w(x)dx$

If w is the function graphed below

Then

$\displaystyle y(x) = \sum\limits_{n=0}^\infty$ $\displaystyle \sin\!\left(\frac{n\pi x}{3}\right)$