Gramps, I don't think I made myself clear enough.
Here is an analogy for what I'm trying to ask.
A common method to measure the rpm of a motor is to put a slotted disk on the shaft and use an LED+photodiode to generate a pulse every time the LED shines through a slot while the motor is running, like this example from the web:
In this case the LED+photodiode are the sensor and if you asked the forum how to measure the number of pulses per second from the photodiode I'm certain that someone would be able to provide you a with a circuit and a program but if this sensor was putting out 2000 pulses per second and you told someone your motor was running at 2000 pulse/sec that would not be very meaningful to them.
That 2000 pulses/sec is the raw value from the sensor and sensors are calibrated so that the raw value can be reported in units that have more meaning to a person. In this case there look to be about 20 slots in the disk so 2000 pulses/sec is 100 revolutions per sec and 100revolutions x 60sec is 6000 rpm which is probably what I would be interested in knowing in this case.
It sounds like your magnet is your sensor so is your project to report something like "my magnet is vibrating like <and here you give some freq or amplitude description> or something more meaningful the the person you are describing it to?
Did you build the air coil just to move the magnet or to does the air coil do something else you are interested in? If so then what does the air coil do?
If the magnet is just the sensor you have chosen to measure what the air coil does then the forum might be able to make more helpful suggestions if we know what you built the air coil to do.
It sounds like the air coil is driven by an amplifier. Do I understand correctly?
If so, where does the signal into the amplifier come from?