Find the general expression for all locations $($x$\text{'}$s$)$ where the deflection is zero along a

railway track that is subjected to a single wheel load. Note: Lecture notes $($pages $36)$

have found only the first $x$ value for the location of zero deflection, but theoretically

there are more locations as one moves further away from the load.

Location of Zero Deflection $(x_2)$

$w=y=\frac{P}{(64EI{k}^3{)}^{\frac{1}{4}}}{e}^{-|x|}[cos(|x|)+sin(|x|)]$

$w=0$ when $(cos|x|+sin|x|)=0$longrightarrow$x_2=\frac{3}{4}$