How to limit a function's cosine value as it approaches 0
$\alpha e^{-\beta x^2}cos(x)$ where $\alpha$ is your peak and $\beta$ is proportional to the strength of the decay
This one's slightly longer and the peak is at $\alpha+1$ but the graph is easier to manipulate:

$cos(x)e^{-\beta x^2}+\alpha e^{-x^2}$