Oscillating plank - Frequency

A plank is oscillating about its center. It rotates between angles $-\theta$ and $+\theta$ and takes time $t$ to complete one oscillation. A cylinder is released on this plank when it is at $-\theta$ and starts rolling down the plank. The oscillation of the plank causes the cylinder to oscillate with amplitude $A$ along the plank.

When happens to $A$ if $t$ is doubled?

Assume that the cylinder never loses contact with the plank.