I've seen plans for a pendulum oscillator water pump that is claimed to pump a large volume of water (100 gallons) from a well of 100 feet deep. The pendulum consists of a 100 pound weight raised 6 feet. A second 20 pound weight is hoisted up a pole 20 feet high. This second weight powers a mechanism which gives the pendulum a very slight push on every swing so that it does not lose any momentum on any stroke. The only energy inputs into this system are the act of raising the 20 pound weight 20 feet and raising the 100 pound weight 6 feet. This is supposed to pump 100 gallons (833 pounds of water) up 100 feet.
It seems to me that this is impossible, because we have applied a given amount of potential energy into this system: 20lbs x 20feet = 400 foot pounds 100lbs x 6 feet = 600 foot pounds So 1000 foot pounds total
So this should be capable (at best) of raising 10 pounds of water (1.2 gallons) up 100 feet.
I've been told that I don't understand the engineering principles of oscillation, and I've been assured that the math checks out. However, based on the very limited physics I know (and I admittedly don't know much) - you can't get more work out of a system than you put in.
How is it possible to get more energy out of a system than you put into it?