Problem 1 Consider the bar depicted in Figure 1. 1. Derive the corresponding expression for the elastic potential. 2. Use the Rayleigh-Ritz method to find approximate solutions considering the...

Please dont answer if you dont answer the whole problem, and can use only python for coding

Extracted text: Problem 1 Consider the bar depicted in Figure 1. 1. Derive the corresponding expression for the elastic potential. 2. Use the Rayleigh-Ritz method to find approximate solutions considering the following approximate displace- ment fields. Comment on your results. (a) û = ax + b (b) й — ах? + ba + c (c) û = ax3 + bx2 + cx + d (d) û = ax + b for 0 < x="">< l/2="" and="" cx="" +="" d="" for="" l/2="">< x="">< l="" 3.="" the="" last="" case="" is="" what="" we="" call="" a="" piece-wise="" linear="" approximation,="" in="" this="" case="" for="" 2="" segments.="" write="" a="" generic="" expression="" for="" the="" potential="" corresponding="" to="" a="" piece-wise="" linear="" approximation="" resulting="" from="" dividing="" the="" bar="" into="" n="" identical="" segments="" of="" length="" l/n.="" show="" that="" in="" the="" limit="" for="" n="" →="" ∞="" the="" approximate="" potential="" converges="" to="" the="" exact="" one.="" comment="" on="" the="" implications="" of="" your="" result.="" 4.="" for="" the="" particular="" case="" where="" p="" 100="" n/m,="" l="0.3," use="" your="" expression="" from="" part="" 3="" to="" create="" and="" plot="" the="" solution="" for="" n="50" in="" python.="" include="" the="400" n,="" q="" 2="" m,="" a="0.0003" m2,="" e="70" gpa,="" and="" v="" source="" code.="" l="" figure="" 1:="" schematics="" for="" problem="">