A simple pendulum with length $L$ and mass $m$ of the bob is vibrating with an amplitude $A$. The maximum tension in the string is
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$\mathrm{T}_{\max }-\mathrm{mg}=\frac{\mathrm{mv}^{2}}{\mathrm{L}}$
$\mathrm{T}_{\max }=\mathrm{mg}+\frac{\mathrm{m}(\mathrm{A} \omega)^{2}}{\mathrm{L}^{2}}$
$=m g+\frac{m}{L} A^{2} \frac{g}{L}=m g\left[1+\frac{A^{2}}{L^{2}}\right]$
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