Determine a1 and a2 for the approximating polynomial and

Question

PROBLEM 1:

Verify thatAEL Is given by the condition   for the problem illustrated:

PROBLEM 2:

The rigid bar ij of length L rests on an elastic foundation. When displaced vertically by v the foundation applies a force f=Kvdx to a length dx of the bar. K is constant find the 2x2 stiffness matrix

PROBLEM 3:

For the governing equation ∂u/∂x + 20 - 16x = 0 in the range 0

1. Determine a₁ and a₂ for the approximating polynomial u^-=a₁x+a₂ x²

2. The percentage errors at x=0.5 and x=0.7 compared to the exact solution of u = 4(e(^-2x)-1)+8x