Prolonged exposure of a protein solution to x-rays results in damage. Often (but not always), this damage presents as aggregation. It is thought that free radicals form on the protein surfaces causing them to stick together. For this reason, we take multiple short exposures and compare the first curve to the final curve.
Oscillation of the sample in the x-ray beam will significantly delay damage, but the effect will always appear if you expose long enough. In this example, we stopped the oscillation to speed up the damage process for purposes of illustration: 
The Guinier plot of the first frame (1) in this dataset is noisy, but otherwise looks fine: 
Notice how the Guinier plot of the final frame (10) has changed: 
Not only has the Rg increased from 13.7 to 17.9, but the I(0) and estimated molecular weight have also increased. Notice also a slight upward smile forming.