Equation that relates gravity and period

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IHaveAQhestion
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I need help with a question on my homework about circular motion. It goes like this:
- Starting from Newton's Second Law, develop an equation for the stopper that relates the force of gravity to the period.
 
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Sorry but it doesn't really show me anything except for a picture of an object spinning horizontally with a mass at the end.

I was thinking about using the F=ma formula but I'm pretty much stuck.
 

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This really has to be reposted with the template filled. I think that filling correctly the "Relevant equations" section of the template will be helpful.

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