Changes

<math>\frac{d^4y}{dx^4}=-(\frac{\rho}{ET^2})\frac{d^2y}{dt^2}</math>

<math>\frac{d^4y}{dx^4}=-(\frac{\rho}{ET^2})\frac{d^2y}{dt^2}</math>

Knowing that the motion of the beam will be oscillatory lets us assume that the solution can be divided into two parts, one representing the maximum amplitude of the motion and the other representing the periodic nature of the motion.

Knowing that the motion of the beam will be oscillatory let's us assume that the solution can be divided into two parts, one representing the maximum amplitude of the motion and the other representing the periodic nature of the motion.

<math>\frac{y(x,t)}{}=y_a(x)e^{i \omega t}</math>

<math>\frac{y(x,t)}{}=y_a(x)e^{i \omega t}</math>

<math>\frac{d^4y_a}{dx^4}=\frac{\rho}{ET^2}\omega^2y_a</math>

<math>\frac{d^4y_a}{dx^4}=\frac{\rho}{ET^2}\omega^2y_a</math>

[[Media:UniformAnalysis.pdf|Uniform-Width Analytical Model]]

[[Media:UniformAnalysis.pdf|Uniform-Width Analytical Model]]