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- WolframAlpha - computational knowledge engine
- HackMD - free online notes tool supporting Markdown language
- Desmos Scientific Calculator - a very handy calculator for everyday usage
- AutoDraw - a simple tool to draw

- Get link
- Other Apps

Vibrating string without damping is represented by the following differential equation: $$ \begin{cases} \begin{array}{l@{\ }l@{\ }l} \frac{{{\partial ^2}u}}{{\partial {t^2}}} = {a^2}\frac{{{\partial ^2}u}}{{\partial {x^2}}} , & \hspace{0.25in} 0 \leqslant x \leqslant L , 0 \leqslant t \leqslant \infty , & \hspace{0.25in} \text{string equation} ; \\ u\left( {0,t} \right) = u\left( {L,t} \right) = 0 , & \hspace{0.25in} 0 \leqslant t \leqslant \infty , & \hspace{0.25in} \text{boundary conditions} ; \\ u\left( {x,0} \right) = f\left( x \right) , \frac{{\partial u}}{{\partial t}}\left( {x,0} \right) = 0 , & \hspace{0.25in} 0 \leqslant x \leqslant L , & \hspace{0.25in} \text{initial conditions}; \end{array} \end{cases} \tag{1} $$ Splitting the string equation into two coupled equations We need to transform the equation: $$ \frac{{{\partial ^2}u}}{{\partial {t^2}}} = {a^2}\frac{{{\partial ^2}u}}{{\parti

This article is based on the Train-platform paradox simlation available at https://train.tdworakowski.com . The paradox If you consider two relativistic phenomena which are length contraction and time dilation , the special theory of relativity may seem inconsistent. Imagine a train 100 meters long is passing a platform 100 meters long traveling at 90% of the speed of light . According to the theory, for the observer on the platform the train is shortened and the time inside it elapses more slowly. But for observer inside the train the length of the train is normal, time elapses normally, however the platform is shortened and the time on the platform elapses more slowly. How is it possible that both of these facts coexist? To answer this question we need to understand the third relativistic phenomenon which is relativity of simultaneity . If we consider these three phenomena together, the theory becomes consistent. You can play with the simulation to confirm that the theory

Here are listed useful PyCharm shortcuts, which I use very often. If you have some other favourite shortcuts, please put it in a comment. Find action Ctrl + Shift + A - find action View Alt + 1 - toggle tool window Project Alt + 7 - toggle tool window Structure Navigation Ctrl + MOUSE LB CLICK - go to clicked object definition / occurences Ctrl + Shift + RIGHT (Linux/Ubuntu) - navigate forward Ctrl + Alt + RIGHT (other OS) Ctrl + Shift + LEFT (Linux/Ubuntu) - navigate backwards Ctrl + Alt + LEFT (other OS) Ctrl + G - go to line Ctrl + N - finds a class by name Ctrl + Shift + N - finds a file by name or path Alt + RIGHT, Alt + LEFT - switch between tabs Alt + UP, Alt + DOWN - jump between functions in code Search / replace Ctrl + F - find string/regexp in file Ctrl + L - move to next occurrence Ctrl + Shift + L - move to previous occurrence Ctrl + R - re

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