A wheel is free to rotate about its fixed axle. A spring is attached to one of i

Question

A wheel is free to rotate about its fixed axle. A spring is attached to one of its spokes a distance r from the axle, as shown in the figure. (a) Assuming that the wheel is a hoop of mass m and radius R, obtain the angular frequency of small oscillations of this system in terms of m, R, r, and the spring constant k.

I've gotten an answer already but I have no idea how it was done. Some people I saw used torque while others used energy. I don't know what to do. A detailed and concise answer would be greatly appreciated.

Explanation / Answer

torwue =I

 

-k(x)r  =  mR2*

a  =R

= -(kr/mR2)x

a/R  = -(kr/mR2)x

a  = -(kr/mR)x

 

2 =   kr/mR

 = (kR/mR)

f  =/2   = (1/2)(kR/mR)

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