Converting Linear Equation to Angular Equation

[mpm]

Can anyone help me convert this linear equation to angular terms?

mx'' + f*sin(x') + kx = 0

x'' = x double dot
x' = x dot

Im having trouble find info on changing this.

 

[mpm]

Well so far I have:

IΘ'' + (g/L)Θ' + ? = 0

I used the small angles approximation which got rid of the sin(Θ').

Can anyone help me turn the kx itno angular terms?
I know x goes to Θ but not sure about the spring constant.

 

[mpm]

I just found something.

Im thinking k = ω^2*m

So that makes this ω^2*m*Θ

and m = I

so my final equation is

IΘ'' + (g/L)Θ' + ω^2IΘ = 0

Does this look right?