Help building something that will go back and forth

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To create a device that moves a wooden rod back and forth like a metronome, a small electric motor with a reduction gear is recommended. The design should include a single linkage connected above the pivot point to achieve the desired motion. The project budget is set at under $50, and it should reach a minimum speed of 200 RPMs. Hobby shops may have the necessary components for this build. Overall, the focus is on a simple mechanism that effectively replicates the metronome's movement.
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Hey
I was wondering if you all could help me. I need to build something that will move a rod of wood back and forth in a fashion similar to a musical metronome.

I am hopeing to make it for under 50 dollars and need it to go about 200 rpms at min.
____
l l
l l
/ l l <----Wood Rod
/ l l
/ l l
/ l l
/ l l
V l l
____________________l___l______________________
l l
l_____________________________________________l

Any help would be greatly appreciated.
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all you need is a small electric motor, perhaps with a reduction gear, and a single linkage attached above the pivot point. Try a hobby shop.
 
I do not have a good working knowledge of physics yet. I tried to piece this together but after researching this, I couldn’t figure out the correct laws of physics to combine to develop a formula to answer this question. Ex. 1 - A moving object impacts a static object at a constant velocity. Ex. 2 - A moving object impacts a static object at the same velocity but is accelerating at the moment of impact. Assuming the mass of the objects is the same and the velocity at the moment of impact...

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