# In the SHM equation $F= -kx$, $k =mw^2$ why not use $mf^2$ where $f$ is frequency $w$ here comes out to be $1/s$ not $\text{rad}/s$?

The reason I am stating this is because on calculating the units of w(omega) I found is equal to s^-1 not regular the rad/s. Proof:

    F=-kx =>  k= -F/x
Newton/metre = (Kg-m)/s^2m = Kg/s^2 (Units of K)


If we take the book definition of kx=mw^2x the we get

                            k=mw^2 then w^2= K/m

Units of this (Kg/s^2Kg)^1/2 = 1/s or s^-1 meaning frequency.


Which makes more sense to me when considering a spring where applying w(angular velocity) seems less effective than f(frequency).

But I'd like to know if I made any mistakes if yes then an explanation would be very appreciated.

Also in this case $$\omega$$ is an angular frequency, not an angular velocity. So you can use either $$\omega$$ or $$f$$. It doesn't matter. They are essentially the same thing. $$\omega=2\pi f$$