When rod is rotated by θ0 and released, then it look this. After roating θ0 and released, when the rod go through mean position it will have maximum speed. Vmax=Aω =r1θ0ω =(
l
3
θ0)ω We know, ω=√
K
I
and I=m(
l
3
)2+
m
2
(
2l
3
)2 =
ml2
9
+
4ml2
18
=
2ml2+4ml2
18
=
ml2
3
∴ω=√
3K
ml2
∴ Tension in the rod when it passes through the mean position is, T=