Why do oscillations deviate from T² ∝ l³ at longest beam lengths?

[lozzyjay]

ok so, my coursework is to measure the oscillations of a mass on a beam to prove that T^2 = k l^3 when k is a constant of proportionality. And basically when plotting the graph of my results, the first 8 results fit exactly on my line of best fit but the last two are completely off. These results where at the longest lengths of the beam. Would this affect the time period in any way? Would it be because there is a greater mass as there is more of the beam oscillating?
Please help!

 

[inha]

The SHM-approximation fails at large oscillations so that's where your model might fail.

 

[lozzyjay]

does anyone know why this is?

 

[siddharth]

lozzyjay, can you think of the reason? When you derived the equation for the time period, what approximation did you use?