I understand conceptually why amplitude doesn't affect frequency (especially when relating to sound - singing louder shouldn't change the frequency of the note I sing). However, the equation for the maximum velocity of an object in simple harmonic motion is $$ v = A \cdot \omega $$ where $A$ is the amplitude and $\omega$ the angular speed.
But I also know that $\omega = 2\pi\cdot f$
So there is an equation $v = A\cdot2\pi f$ that relates amplitude and frequency but they don't have a relationship. How?