How to replicate this photocopier distortion effect?

For a way to mimic this using vectors in Illustrator, this would be how I’d pursue it…

• Set Type (no need to convert to outlines. In fact it may be better if you don’t)
• Select the type with the Selection Tool (v)
• Choose Object > Envelope Distort > Make with Mesh
• Set a number of rows and columns that seems appropriate (you can always change this later so just “best guess” here)
  
• Now, using the Direct Selection Tool (a) (white arrow), Select and move the mesh points to create “stretches’ within the type. If needed, you can use the Gradient Mesh Tool (u) to add more mesh lines.
  
  Just focus on the vertical stretching to start.
• When you’ve got the stretching as you’d like, select and move groups of mesh points horizontally to create the “wobble”, again, adding more mesh divisions if needed.
  
• Then you can address things like color fades and diffusion via an Opacity Mask (click for more info on that)
• Because this is still Live Type, you can go back and choose Object > Envelope Distort > Edit Contents to change the type at any time
  

I’m not stating this is perfect, but it is far more controllable and completely vector. Unlike a scan that’s been tugged a bit while being scanned. It all comes down to your desired end goal.