Chapter 2, Problem 24E

Consider the tapered bar in problem 17. Use the Rayleigh-Ritz method to solve the same problem. Assume the displacement in the form of $u\left(x\right)=a_0+a_{1}x+a_2{x}^2$. Compare the solutions for $u\left(x\right)$ and $P\left(x\right)$ with the exact solution given below by plotting them. $u\left(x\right)=\frac{Fx}{\pi Er\left(0\right)r\left(x\right)},P\left(x\right)=EA\left(x\right)\frac{du}{dx}=F$