I drive a used 2009 Toyota Matrix S (80k miles), and this is my first manual transmission car so forgive me if I'm describing something obvious and pedestrian here.
Recently, I've noticed some odd behavior when letting the clutch in to start from a stop: although everything is fine and smooth when I hold at 2000 RPMs, if the RPMs drop to 1300-1600, the clutch pedal will judder for a second as if I'm lugging the engine, until the clutch fully engages. However, I've never seen the engine lug over 1200 otherwise, even under heavy acceleration in 5th.
Worth noting is that this only happens when I'm accelerating and engaging the clutch relatively hard - one of those "oh shit, the light turned" situations we've all had. I don't experience this during light acceleration at all, and my solution when I need a little power from a stop has been to just peg the engine somewhere between 2000-3000 RPMs and slip the clutch a lot.
Now I'm no mechanic, but my instinct is that this is somehow to do with the added strain on the clutch. I'm not dropping it, but I wonder if the heavy load is accentuating some sort of mechanical warp or weakness, courtesy of either the previous owner or a long service life. I'm guessing the solution either way is "be nicer to your clutch."
But, I'm still curious: Why might my clutch be pulsing under heavy loads?