How did the subwoofer before blew? The amp must have problem (possibly clipping) to cause the sub to blow if it didn't do that previously. When an amp clip, it can send more power to the subwoofer, which in turns, the heat from that extra power can blow the voice coil of the sub.
Swap the amp and see if the problem exist. If the problem is gone, then the old amp is probably broken. If it still doesn't fix the problem, then the problem lies within the wiring of the speaker. That pulsing action seems like the amp is clipping and clipping would mean overdriving the amp. That would cause the subwoofer to excurt out a lot.
Swap the amp and see if the problem exist. If the problem is gone, then the old amp is probably broken. If it still doesn't fix the problem, then the problem lies within the wiring of the speaker. That pulsing action seems like the amp is clipping and clipping would mean overdriving the amp. That would cause the subwoofer to excurt out a lot.