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PHP JQUERY PROXY DEMO

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Proxy script (or proxy program) is a script, wich is located between the user's browser and the "target server". Here I'would like to make a simple demo for PHP-Jquery-script proxy method. So far in my blog I just use YouTube API v.3 and JavaScript-jQuery to find videos. This time I try to use PHP language and jQuery to find videos. We often hear about "Web scraping with PHP," which can be roughly considered to include 9/10 PHP and 1/10 jQuery. Now I want to do it again but with 1/10 PHP and 9/10 jQuery. This page ("php-jquery-proxy.html") is for web scraping using mainly jquery-ajax in combination with only one function from PHP language (get_file_contents function). Using it I can get video ids, video titles from the source code of youtube pages and watch those videos continuously. To use this page you don't need to have Youtube API-3 key but need to download from Internet the XAMPP package...
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EXAMPLE ON MODIFYING HTML5 MEDIAELEMENT.JS PLAYER

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Creating a video player using HTML5 is not too difficult. But it only plays some video formats such as MP4, OGG, WEBM. To watch more video formats, we must use the HTML5 video player plugin. I tried "Mediaelement.js" and found it great: in addition to the above mentioned formats, it can play YouTube, DaylyMotion, SoundCloud, Facebook, Vimeo, HLS, Dash, FLV and others. In the samples by "Mediaelement.js" I choose only two examples close to satisfy my needs. However in the sample for playlist, the player only plays mp4, mp3, ogg, webm and youtube. Meanwhile, the demo file can play a lot of formats but only play 1 video (when it is clicked) and stops. All the scripts are very short. Most just include only one function with multiple arguments to build the player. Nothing more. So I looked at the source code of the "mediaelement-js.com" page, where all js files are online and have more functions. However, it is very difficult for me...
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PLOTTING FUNCTION GRAPH USING JAVASCRIPT (Part 2)

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Note: Please wait a bit for the math formulas to appear.(I use MathJax.js) 1- Problem 1: A spring-mass system on horizontal surface performs damped oscillation due to Coulomb frictional force \[F_{cl}=\mu mg\]. When t = 0 the mass was pulled so that the spring stretches a segment of $x_0=6$ (cm) then it was loosed. It's known that: \[\omega = \sqrt{\frac{k}{m}}= \frac{\pi}{4} = 0.7854 \quad\text{(rad/s)}\] and the length of the way for one direction movement (from left to right or from right to left) decreasing steadily to 0.8 (cm). a- Establish the equation of motion x = x(t) b- Using LaTeX to draw this oscillating graph. 2- Solution: A. Two half periods at the beginning We will use the horizontal x axis in the direction of elongation of the spring. x = 0 is the position of the mass when it is not pulled or compressed. The condition for the mass to stop is: \[\text{velocity }v=0\quad\text{and}\quad\ |x| \le d\quad\text{where }d = \f...
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