Can somone explain this review solution (vibrations)?

[whitejac]

Homework Statement

Homework Equations

The equations are all given

The Attempt at a Solution

This isn't really a homework question... it's solved, but I'm having a hard time following it. I don't understand where the first term:
-a(kaθ)

comes from. I can see it's the moment relation between the hinge and the spring but why is the a term squared?

 

[Nidum]

Value 'a' is used to relate the force generated by the spring to the angle θ and as the lever arm length for the moment about the pivot generated by the spring force .

 

[whitejac]

View attachment 197634Value 'a' is used to relate the force generated by the spring to the angle θ and as the lever arm length for the moment about the pivot generated by the spring force .

Looking at it again. I'm sorry. I think my problem was just misreading the answer.
Value a just the value used to reference the length? (6in)

This would make:
F _spring = xk
x = aθ

Thus a(kaΘ) = M
And it's negative because the fbd assumes the weight is tending CW while the weight and the spring force tend CCW?