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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Welcome to PF.

Our rules for homework say that you must show us your work before we can help.

What equations would you use?

Show us your attempt.

Do you have a diagram? You can post it with the UPLOAD button.
 
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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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It also shows a weight that presumably can pull the string through the tube making the radius of rotation shorter.

PS: Stopper?
 
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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