# Plotter - examples

Some examples of plots created by plotter, just to get an idea what it might be good for. The images on this page are drawn on the fly: the URLs of the plots (yes, the ugly one with the ridiculously long query string) were created once in the UI part and copied into the src-attribute in an image-tag (see the page source for an example).

Whenever the page is loaded or reloaded, the plotter creates images and serves them to the browser.

A plot of a single period of sine and cosine ($$x$$ in the range of $$0$$ to 2$$\pi$$). The settings used for this plot are

• function 1: $$\sin(x)$$, range $$0$$ to 2$$\pi$$, legend shown
• function 2: $$\cos(x)$$, range $$0$$ to 2$$\pi$$, legend shown
• background Color is white with black captions and a grid in #f2f2f2
• plot ranges: $$x$$ from -1 to 2$$\pi$$ +1, $$y$$ from -2 to 2
• local maxima/minima are shown as additional points

This is a plot showing the movement of an underdamped harmonic oscillator: $$y(t) = A \cdot e^{-\gamma t} \cos(\omega t + \phi)$$ for a linear damping force $$F = -c\cdot v$$ and a damping coefficient of $$\gamma = \frac{c}{2m}$$. Underdamping occurs when the damping coefficient is lower than the undamped resonant frequency of the oscillator.

For the example plot an amplitude $$A = 4$$, a phase $$\phi = 0$$, damping coefficient $$\gamma = 1/3$$ and a frequency of $$\omega = 3$$ was used.

The switching process at $$x=0$$ is modeled by a Heaviside function.

Here's a real-life example: a plot of a rational function created for one of my basic maths tests

• the function used is $$f(x) = \frac{x}{x^2+1},$$ plotted from -8 to 8
• axis and tick marks in Grey
• a local minimum, a local maximum and the function's points of inflection (labeled W) are shown

Just to show the possibility, the last plot is a bit more funky (yeah!): this is a gaussian distribution centered around 2 with a variance of 1. The area below the curve is filled and the image is blurred and embossed by GD's filters. Finally the whole plot is rotated clockwise by 10°.