The correct option is D mg(1+α2m)
The tension is maximum when the bob is in the mean position and is given by T=mg+mv2l where l is the length of the string.
Now, vmax=|Aω|=(lαm)ω=lαm√gl
⇒v2max=l2α2m×gl=lgα2m
∴Tmax=mg+ml×lgα2m=mg(1+α2m)
Hence, the correct choice is (d).