harmonic oscillator - Oscillation with exponentially increasing period

I am trying to build a model for a certain type of oscillatory behaviour with a kind of exponential dilatation.

How can I modify the function of a simple cosine oscillation $\psi(x)=A_0 \cos(2\pi\; \omega x)$ to an oscillation which period would increase exponentially along the abscissa from left to right?

Answer

I've turned my comment into an answer so the question can be closed.

A very similar question was asked and answered here.