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I hate to point you toward ebay, but it may be the easiest way to achieve what you want without much electronic assembly, provided you're happy with a very basic solution that cannot be easily extended:
This module may help:
It has a couple of adjustments (the blue blocks are variable resistors, adjustable with a screwdriver), that can be used for adjusting the on/off speed. It won't quite reach once every 5 seconds, but can be modified to do so by changing one part, if you're willing to solder or can find someone nearby to help you.
If you wanted a larger control knob then those variable resistors need to be unsoldered and replaced with larger ones attached to wires, so would need some soldering.
It cannot control a motor on its own, so you'll also need this:
This will take the output from the first module, and interface it to the pump motor (i.e. to the 7.5V connection to the pump).
Lessening the voltage will decrease the speed of the fan, but it might become ineffective once slowed to a certain speed.
Maybe others have better suggestions, e.g. some board or product that could be modified to do what you want, with little construction.
Also, once you start wanting to do more complex things (like precisely control on/off times or have more flexibility in speed and on/off patterns) then really it needs a programmable solution, not something simple like the ebay items mentioned.
For that, it would be good to use something like an Arduino (it could be used with that second board).
It entails programming, but would be the far more flexible solution. I'd personally go the Arduino route, because of the high likelihood that the first option would be too inflexible once you start wanting slight changes - the first option cannot be modified to do arbitrarily programmable behaviour.
The simplest preassembled timer would be an industrial timer relay, for example these or these. You want one with a "repeat cycle" function, where you can separately set the on and off times, and it will endlessly repeat that cycle. The relay itself will require a power source greater than your pump will (the simplest thing is to just use 120 VAC from the wall), but it can switch any other voltage you need to power your pump. I would use an adjustable DC power supply to power the pump, so that you can fine-tune the speed.
I would opt to use an arduino, to control everything,
using some relatively simple programming you can control the fan on time off time, speed plus other options, i believe you would have a lot more control over it also.
You would need to add a relay or transistor to turn the unit on and off, as the arduino cannot handle that sort of power, but you could with a power regulator reduce that 7.5v down to run the arduino
I have a technical 'problem' which a Farnell employee thought might be worth posing to the community on here.
I am an artist and I am looking to make a 'breathing' sculpture.
I have started by buying a battery operated air pump (designed for mattresses etc.) which has a power supply input bit so that the batteries (7.5V DC 300mA) can be re-charged when the pump is not in use.
What I had hoped to be able to do was re-wire the pump to include a) a dial which allows me to lessen the speed of the fan (or can this be done by using lower voltage batteries?) and b) to solder in a sort of intermittent timer so that the fan comes on and off every 5 seconds or so, giving the impression of breathing.
If anyone can help with this I would be very grateful! I don't have much of a budget... :-)