Angular amplitude of a simple pendulum is ${\mathrm{\theta }}_0$. Maximum tension in the string for small ${\mathrm{\theta }}_0$ will be:

$$\begin{gathered} \mathrm{T}-\mathrm{mg}=\frac{{\mathrm{mv}}^2}{\mathrm{l}} \\ \mathrm{But} {\mathrm{v}}^2=2\mathrm{gl} \left(1-\cos {\mathrm{\theta }}_0\right) \\ \mathrm{So} \mathrm{T}=\mathrm{mg}+2\mathrm{mg}\left(1- \cos {\mathrm{\theta }}_0\right) \\ \mathrm{T}=\mathrm{mg}+2\mathrm{mg} \left(2 {\sin }^2 \frac{{\mathrm{\theta }}_0}{2}\right) \\ \mathrm{T}\approx \mathrm{mg}+4\mathrm{mg}{\left(\frac{{\mathrm{\theta }}_0}{2}\right)}^2 \\ \mathrm{T}\approx \mathrm{mg}\left(1+{\mathrm{\theta }}_0^2\right) \end{gathered}$$