Past exam of the mathematical mechanical biology course of the University of Oxford / 2023 / 3 / a / i / Solution

Before contact with both walls, the elastic rod can grow freely, so its elastic stretch ratio is $\alpha =1$ and its length is its stress-free grown length,The first contact occurs when $\ell (t_c)=L_1$. For the intended growth case $c>0$,The condition $L_1>L_0$ ensures $t_c>0$. If $c=0$, contact never occurs; negative $c$ describes shrinkage rather than the stated continuing growth.