Ignoring the fact that you posted a picture to a non-binaries group:
Brent, The motion you are talking about is called reciprication. Reciprication is done with an offset shaft. Look at the way a locomotive drives its wheels. The motor would only need to go in one direction, if you needed feedback, you can sense the two positions. Delay would be from either a microcontroller or a set of one-shots.
See howstuff works for an explaination and animation:
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Scott
Hello there Folks.
>
> I need some advice as to how I would make a small dc motor (say that ran on
> 2 c cell batterys) that would mimic a windshield wiper motor with a delay. >
> 1. This motor would have to lift a .25 pound weight
> 2. The motor would travel one 1/2 turn clockwise, then travel back 1/2 turn
> in 2 seconds, and then delay for 10 sec.
> It would be cool if the delay could be set to 5 second intervals from 1
> second to 5 minutes.
>
> Enclosed is what I have envisioned as my final product.
>
> Figure 1 shows my staring position
> Figure 2 shows my mid Position
> Figure 3 Shows my 1/2 turn
> Figure 4 shows my resting position with a 1 second delay,
> Then it repeats the process,,,
>
> Thanks ...
>
> Brent
>
> enclosed is a picture of what the finished product might look like..