I have a simple sine function:
y = sin(x) + 1
How can I modify the equation, or even add/ multiply with another equation, such that if I change a parameter, only the amplitude on the top increases/ decreases? The bottom remains at y = 0.
Increase amplitude only on one side of a sine wave
trigonometry
Related Solutions
If you want the absolute maximum amplitude and the $\beta$s are such that the peaks can line up, you can just sum the individual waves. They don't line up perfectly very often and less often as more sine waves are included. Another approach is to do a root sum square of the individual amplitudes. This gives you a better feeling for the real amplitudes you will see, but will not be the maximum. If you go to Alpha you can plot it or again. The first has all the peaks lining up at $t=0$, the other has some delays added.
Plot[ x (1 - Sin[x]), {x, -1, 45}, GridLines -> Automatic]
You can adjust the slope $m$ of envelope, time period etc as:
$$ y= m x \;(1- \sin \dfrac{2 \pi x }{\lambda})$$
To reflect about x-axis making it go down, equation can be changed as:
Plot[ x (-1 + Sin[x]), {x, -1, 45}, GridLines -> Automatic]
Best Answer
$y = \alpha \left( \sin(x) + 1 \right)$ for $\alpha > 0$.