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Hello all. I make a semi long drive every weekend. Past two weeks, after the first 20 minutes of driving with no issues, I'll hit a 20 min stretch at speeds going 65 plus where I get a pretty good shake/vibration/helicopter thump sound throughout the car and steering wheel. It continues when decelerating and there is a pulsing in the brake pedal when applying them.

After a few iterations of accelerating and braking at lights for that 20 min stretch of time, it just stops and doesn't happen again for the rest of my hour and a half drive. I replaced the brakes and rotors 7 months ago, and I can't understand why a motor mount, caliper or transmission will be fine for 20 mins, act up for 20 mins, and then be fine for an hour and a half.

What the heck could this be?

 
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rotate tires around, see if sound moves

 
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Will do.
I was reading around a bit. Can the ABS be activating while on the gas pedal? And that would cause the pulsing in the brake pedal when I do eventually apply them? There's no light and I really don't have a prior experience with ABS activation, so I don't know how it's supposed to feel.

 
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Probably a warped rotor, maybe a sticking caliper

 
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just get car over wet grass and stomp on brake pedal, you will quickly find out how it feel

Even a worn out tie rod can make vibrations during braking (wheel will start moving)