Capacitors 2/9

On Thursday we learned about capacitors. Capacitors store voltage.  In our circuit, the voltage of the  capacitor increases until it is the same as the voltage in the circuit. But, since the voltage of the capacitor approaches the overall voltage asymptotically I don’t think it ever actually reaches the overall voltage.  As the voltage in the capacitor increases the current decreases, asymptotically approaching zero.
Here is a picture of the circuit we built:

    We just added a capacitor to the circuit that we had built on Monday, and it became an oscillator. We also changed the circuit so that output voltage went through a resistor and fed back into the op-amp as one of the inputs.  Our professor called what we built an op-amp with hysteresis. The important part  is that the op-amps output voltage switched between -12 volts and +12 volts. Consequently the capacitor oscillated between wanting to have its voltage be -12 volts and +12 volts.
   Then we put a speaker on the circuit so that the voltage of the capacitor went into it. We could change the pitch of the tone coming out of the speaker by changing the resistance with our potentiometers, which was pretty fun.
    After class I was pretty confident I understood what the circuit was doing, but the more I thought about the less I understood it. The more I try to write about it the more my confusion is deepened. Which left me wondering, could you still use an oscillator in a larger project even if you didn’t really understand how it worked? How far can you take this concept of  abstraction?