Question: For a > b:
−Pb(L² − b²)³/²
───────────────
9√3EIL
at xₘ = √((L² − b²)/3)
graph: formula block, position_hint=top-left
using this formula
1. **State the problem:**
We are given the formula
$$\frac{-Pb(L^2 - b^2)^{3/2}}{9\sqrt{3}EIL}$$
and the position
$$x_m = \sqrt{\frac{L^2 - b^2}{3}}$$
We want to understand or analyze this formula and the position $x_m$.
2. **Explain the formula:**
This formula likely represents a physical quantity (such as deflection or stress) depending on parameters $P$, $b$, $L$, $E$, $I$, and $L$ again.
- $P$ and $b$ are variables or constants.
- $L$ is a length parameter.
- $E$ is Young's modulus (material property).
- $I$ is the moment of inertia.
The numerator involves $(L^2 - b^2)^{3/2}$ which means the quantity depends on the difference of squares raised to the power $3/2$.
3. **Position $x_m$:**
The position $x_m$ is given by
$$x_m = \sqrt{\frac{L^2 - b^2}{3}}$$
which is the square root of one-third of $(L^2 - b^2)$.
4. **Interpretation:**
This formula might be used to find the maximum value of some quantity at position $x_m$ along a beam or structure.
5. **Summary:**
- The formula is
$$\frac{-Pb(L^2 - b^2)^{3/2}}{9\sqrt{3}EIL}$$
- The position where this applies is
$$x_m = \sqrt{\frac{L^2 - b^2}{3}}$$
No further simplification or calculation is requested.