Answer
No, the time period, $T$ is not linear function of length, $L$.
Work Step by Step
Using the data we get $T(20)=0.9$, $T(30)=1.1$ and $T(40)=1.27$.
If the function is linear then, the change in time period with respect to change in length must be constant, i.e., $\dfrac{\Delta T}{\Delta L}$ must be constant.
But we have
$\dfrac{T(30)-T(20)}{30-20}=\dfrac{0.2}{10}=0.02$ while $\dfrac{T(40)-T(30)}{40-30}=\dfrac{0.17}{10}=0.017$, which clearly indicates that the function is not linear.
