OK so if you look at the back of your subwoofer (Pic3) at Input One, you will see there are inputs from the amp/receivers front speaker terminals. The speaker outputs are then connected to the front left right speakers.
This configuration is really to allow connection of a stereo amplifier that has no dedicated subwoofer out. What happens is the sub receives the left/ right signals. The bass is filtered out and sent to the sub and the the rest forwarded to the front speakers.
Connecting an RCA cable to Input Two there is no signal being sent to the speaker outputs on Input One.
You may have to consider buying another amp to power the transducer. You would connect the other sub out on the receiver to an input on that amp then connect the speaker terminals to the Aura shaker which can now be independently controlled by that amp.
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