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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.?

enter image description here

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

Martin Erlic
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1 Answers1

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

enter image description here

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

Simply Beautiful Art
  • 74,685
  • I can see visually that the lower peaks are 10% of their original value. But how can I determine this? Say I want to set it to 2%. I guess I'm not seeing the relationship... – Martin Erlic Oct 12 '16 at 14:33
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    @santafebound See the extra $\frac{11}{20}(1+\frac12\cos(\pi x))$ I put in the formula? Graph that part alone and manipulate it as you need it to be. You'll note the nature of its peaks to be at $1$, so it won't affect the positive peaks. But the bottoms will be at $0.1$, multiplying the original function by $0.1$ at the bottoms. – Simply Beautiful Art Oct 12 '16 at 20:38