Proof of Equation for Period of Spring: T = 2pi (root x)/(root a)

[decamij]

I just want to know if the following proof is okay. I'm in grade 12, and i this will probably be on my midterm.

Prove the following equation (for the period of a spring):

T = 2pi x (root)x/(root)a

If: ac=v^2/r, and v = 2pirf, then:

ac = 4pi^2rf^2, and:

ac = (4pi^2r)/T^2. Therefore,

T = root(4pi^2r)/a

Therefore,

T = 2pi (root x)/(root a)

 

[aekanshchumber]

You equated it in a good manner but I don't thik it is good. You have taken centripetal acceleration in account but in an oscilating spring it is not possible.
To find it correctly, use t = 2 (pi)/f
find f for spring motion.

 

[decamij]

But something in uniform circular motion and an ideal spring are both examples of simple harmonic motion

 

[aekanshchumber]

yes, that's right, oscilating motion is also called as the projection of the circular motion. But when you are giving a proof for oscilating spring than you must take only spring i system in account, you can reffer to other relative systems, but relate them with the required system.
this proof is good to relate the circular motion and the oscillating motion but not good to obtain nice marks.