Asymmetrically driving a sine wave?

Question

I was looking into damped sine waves and I was wondering, what parameter of the function controls for the amplitude of the wave on either side of the x-axis? For example, if I wanted to make a graph where the minima below the x-axis were closer to the x-axis than the maxima above the x-axis, how would I do that? Specifically, how would I make the minima below the x-axis only 10% of the size of peaks above it, i.e. over 10, under 1, over 20, under 2, over 30, under 3, etc.?

https://graphsketch.com/?eqn1_color=1&eqn1_eqn=(1%2F4)e%5E(x%2F3)(cos(1*(pi)*(x)))&eqn2_color=2&eqn2_eqn=&eqn3_color=3&eqn3_eqn=&eqn4_color=4&eqn4_eqn=&eqn5_color=5&eqn5_eqn=&eqn6_color=6&eqn6_eqn=&x_min=-17&x_max=17&y_min=-10.5&y_max=10.5&x_tick=1&y_tick=1&x_label_freq=5&y_label_freq=5&do_grid=0&do_grid=1&bold_labeled_lines=0&bold_labeled_lines=1&line_width=4&image_w=850&image_h=525

The function above: $\frac{1}{4}e^\frac{x}{3}*\cos(\pi*x)$

Answer 1

Try $f(x)=\frac{11}{80}\left(1+\frac12\cos(\pi x)\right)e^{x/3}\cos(\pi x)$

The positive peaks are the same, but the lower peaks are now $10\%$ what they used to be.