# Zbigniew Kąkol

Website

## Computer simulations ....

The software (all programs) is provided as is. This software has been written with great care but we do not warrant that the software is error free. In no event shall we, the authors, be liable for any consequential, special, incidental or indirect damages of any kind arising out of the performance or use of this software.
Click on the program name to download it. For short description of the program move cursor over the icon next to the program name.

This program shows motion (along straight line) with constant acceleration as a function of initial velocity and acceleration. You can trace instantaneous velocity, position and displacement of a moving object.
This programs shows projectile motion as a function of initial velocity and launch angle. Instantaneous velocity and acceleration (and their components) are displayed.
The program illustrates calculation of the work done by a variable force F(x) which changes with distance. In program you can divide displacement into short segments. In the limit, as the segments becomes very small, we get a definite integral (are under F(x)), which we define to be the work W.
This program illustrates one dimensional collision between two balls. You can adjust initial velocity of colliding balls, their mass m and coefficient of restitution.
This program shows two hard balls colliding, one moving, one at rest. You can adjust initial velocity of the striking ball, ratio of masses and impact parameter.
This program illustrates a motion of a mass suspended on a spring. You can adjust spring constant k, mass m and the amplitude of the motion. Watch the changes of displacement, velocity, kinetic energy, potential energy, and total energy.
Watch simple pendulum motion as a function of pendulum length, motion amplitude, and damping constant. You can change option to critical damping or aperiodic motion.
This program displays a result of superposition of two transverse waves as a function of amplitude ratio and phase shift. Additionally you can watch standing waves and beats.
This program shows Doppler effect for sound waves in the case when source and receiver move either directly toward or directly away from each other, at speeds less than the speed of sound. You can change speed of the source and receiver as well as source frequency.
This program plots the Maxwell speed distribution for a given temperature. You can compare plots generated for two selected temperatures.
This program illustrates mixing of two gases, initially placed in two containers, as a function of the temperature. In the program you can trace actual concentration of gases and molecules speed distribution compared with the Maxwell speed distribution.
This program shows electric field lines and electric potential due to given static configuration of point charges. You can select particular charge configuration or create your own charge arrangement.
This program shows charged particle path in uniform magnetic field B. You can adjust magnitude of magnetic field B, particle velocity v, and angle between v and B.
This program simulates voltage drops across each element of the circuit R, L, C in comparision with applied voltage U(t) and the current I(t). The circuitt parameters: R, L, C and a frequency f of applied voltage may be changed. Particularly, you can adjust either the frequency f of the source or natural frequency of the circuit (by changing L and C) to reach the resonance state.
This program illustrates the direction of the incident, reflected, and refracted rays at a flat and smooth interface surface between two materials in terms of the angle of incidence and refractive indexes n1, n2.
This program illustrates graphic construction of images formed by converging and diverging lenses. Using proper control you can change position of lens and object. You can also change focal length.
Watch interference of two coherent light waves resulting from sending a wave through two very narrow slits. You can change a distance between slits, wavelength, and a distance from slits to screen.
This program displays the diffraction pattern of plane waves of light that are diffracted by a single slit. You can change a width of a slit, wavelength, and a distance from slit to screen.
This program displays the diffraction pattern of plane waves of light that are diffracted by two slits. You can change a distance between slits, wavelength, a width of a slits, and a distance from slits to the screen.
This program illustrates plane polarized electromagnetic wave, which propagates in Y direction. The electric field vectors E, are parallel to the Z axis, whereas the vectors of the magnetic field B, are parallel to the X axis. You can adjust wave lenght and amplitude of the fields.
The program plots blackbody radiation spectrum for a given temperature. You can compare plots generated for two selected temperatures.
This programm visualizes the photoelectric effect experiment with photocell circuit. In program, you can adjust a voltage placed across the electrodes of photocell, light intensity, and light frequency (in the visible and ultraviolet range).
The program illustrates spontaneous transformation of radioactive nuclei. You can watch how the number of radioactive nuclei in the sample is changing with time. You can adjust a half-life of a radionuclide.
This program plots (for selected quantum numbers n, l, m) the radial part of hydrogen atom, the radial and angular probability distribution function, and the visualization of hydrogen atomic orbitals in two dimensions.
 Motion with constant acceleration Projectile motion Work done by a variable force One dimensional collisions Two dimensional collisions Simple harmonic motion Damped simple harmonic motion Superposition of waves The Doppler effect The Maxwell speed distribution Diffusion Electrostatics Charge particle path in the magnetic field RLC series circuit Reflection and refraction of light Lenses Interference of light Single-slit diffraction Double-slit diffraction Electromagnetic wave model Blackbody radiation Photoelectric efect Radioactive decay Wave functions of hydrogen atom