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I believe you made an error in your 3 from last equation. The sum of the forces is equal to ma, not -ma. The equation you derive is not unitarily correct. The period should be equal to 2*pi*sqrt(7r/5g)

Physics

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I am teaching or have taught AP physics B and C [calculus based mechanics & electricity and magnetism] as well as Lab Physics for college bound students. I have a BS in Physics from the University of Pittsburgh and a Master of Arts in Teaching from same. I have been teaching physics for 34 years. I am constantly updating my skills and have a particular interest in modern physics topics.