### 6.2 Some Functions $Math content$ that are important in Physics

The following simulation shown in Fig.6.3 uses the basic structure of the previous example.

In this simulation some important formulas of physics of the type $Math content$ are shown, whose parameters have been chosen in such a way, that the variable $Math content$ and the adjustable parameters correspond to simple, physical quantities. In the second column of the following table the well known formulas from physics are given and the formulation in the simulation syntax is given in the second line. Calling the function random(n) creates a random number between $Math content$ and $Math content$. A random distribution with maximum deviation that is symmetric to zero is obtained as random(n)-n/2.

In the third column the meaning of the corresponding variable $Math content$ and the parameters used are given. Gaussian

 Gaussian $Math content$ $Math content$ standard deviation $Math content$ area normalized to 1 1/(a*sqrt(pi))*exp(-((x-b)/a)ˆ2) $Math content$ symmetry variable Gaussian $Math content$ + noise $Math content$ standard deviation $Math content$ with additive noise 1/(a*sqrt(pi))*exp(-((x-b)/a)ˆ2) + $Math content$ symmetry variable random(c/10) - c/20) $Math content$= maximum added noise Gaussian $Math content$ noise$Math content$ $Math content$ standard deviation $Math content$ with multiplicative 1/(a*sqrt(pi))*exp(-((x-b)/a)ˆ2) *(1 $Math content$ symmetry variable noise random(c/10) - c/20)) $Math content$= maximum multiplicative noise Poisson $Math content$ $Math content$: expectation value of $Math content$ distribution (x+10)p^*exp(-x-10)/faculty(p) $Math content$= 1,2,3,$Math content$ amplitude $Math content$ $Math content$ angular frequency modulation a*sin(10*x)*cos(b*x) $Math content$: carrier frequency bx:modulating frequency phase $Math content$ $Math content$ angular frequency modulation a*sin(10*x)*cos(b*x) $Math content$: carrier frequency 2bx:modulating frequency frequency $Math content$ $Math content$ angular frequency modulation a*sin(5*x*cos(b/10*x)) $Math content$: carrier frequency b/10 x:modulating frequency special theory $Math content$ x = $Math content$ = v/c of relativity: sqrt(1-xˆ2) $Math content$: velocity length change $Math content$: speed of light special theory $Math content$ x = $Math content$ = v/c of relativity: 1/sqrt(1-xˆ2) $Math content$: velocity mass change $Math content$: speed of light Planck’s $Math content$ $Math content$ = wavelength $Math content$ in $Math content$m radiation law a*23340/(x+2)ˆ5/(exp(8.958/((x+2)*b))-1) $Math content$: scale factor $Math content$: temperature in $Math content$ K

For calculating the factorial $Math content$ this file contains some special code; in other simulation files this function cannot be used.

Fig.6.3 shows a normalized Gaussian impulse with additive noise superimposed on it, and its integral, that in spite of the perturbation reaches $Math content$ quite smoothly and accurately. The formula field can be edited, such that functions can be changed or other functions can be filled in.