Regard the diff equation that includes $sin(\phi)$:  $mϕ′′+aϕ′+(mg/L)sin(ϕ)=0$  $ϕ(0)=0.1$  $ϕ′(0)=0$  where $m=0.1,L=1,a=2,$  How can i rewrite the second order diff equation as a system of first order linear equations?
Regard the diff equation:  $mϕ′′+aϕ′+(mg/L)ϕ=0$  $ϕ(0)=0.1$  $ϕ′(0)=0$  where $m=0.1,L=1,a=2,$  1) Rewrite the second order diff equation as a system of first order linear equations.  2) What is the matrix that comes from the rewritten equations?
How do I detect when someone shakes an iPhone? I want to react when somebody shakes the iPhone. I don't particularly care how they shake it, just that it was waved vigorously about for a split second. Does anyone know how to detect this? Does the limit $\lim _{x\to 0} \frac 1x \int_0^x \left|\cos \frac 1t \right| dt$ exists? Does the limit $\lim _{x\to 0} \frac 1x \int_0^x \left|\cos \frac 1t \right| dt$ exists ? If it does then what is the value ?   I don't think even L'Hospital's rule can be applied . Please help . Thanks in advance Usage of the word "meet" in the context of a phone call/video conference Upload images from the Stack Exchange Android app I would like to request implementation of uploading images to questions/answers from the Stack Exchange Android app, especially now as it would definitely help uploading screenshots for reporting bugs and feature requests. RSA, DES, AES, etc., all use (relatively) complicated mathematics to encrypt some message with some key. For each of these methods, there have been several documented vulnerabilities found over the years. Some even believe that there is a vulnerability in AES known only to the NSA.  On the other hand, the one-time pad is not only ridiculously simple, but also has been shown to be impossible to crack (if used appropriately).  Say you have some message to be encrypted with length n. Simply generate a random string with length m where m is at least as large as n, and perform modular addition of the random string onto the message.  As long as the random string is generated with a high-enough-quality random number generator, and as long as the same one-time pad isn't reused, it should be impossible to crack.  If this is true, all we would need to perfect are fast, cryptographically secure deterministic random number generators. Use the key as a starting seed for the RNG and you have a powerful uncrackable encryption scheme which is simple to understand and implement.  Blum-Blum-Shub is a fast, cryptographically secure PRNG, and there are others too.  I have written a C++ program which uses two 2048-bit primes (which match the necessary criteria) for Blum-Blum-Shub and uses a password which the user enters - converted into a starting seed - to run byte-wise modular addition. The process is fast, deterministic, and if the literature I have read is correct then it should be very secure.  So why is so much time and effort invested in coming up with convoluted encryption cyphers when mathematics shows that the simplest is often the best? So I need to compress a directory with max compression.   How can I do it with xz? I mean I will need tar too because I can't compress a directory with only xz. Is there a oneliner to produce e.g. foo.tar.xz? I have the low battery alarm disabled in the BIOS settings on my Lemur laptop, but the alarm still sounds when the battery is low.  The sound is a very loud and annoying beep that repeats every couple seconds. The laptop will last another 20 minutes without being plugged in so the battery level isn't properly being detected anymore anyways. I found that if I mute my audio then the beep stops but I obviously cannot listen to anything anymore. If i turn the volume back on even to just 1% the battery alarm is audible again at full volume.  I remember there used to be a mixer somewhere that could control the internal speaker and so if I could find that again then maybe i could mute that and fix this problem.   I have Ubuntu 14.04.  Note that I'm not talking about a low battery notification, which is something through gnome; as opposed to a low battery ALARM which is this very loud beep every couple seconds coming through the internal speaker.  Nevertheless, here are my gnome power settings:  $ gsettings list-recursively org.gnome.settings-daemon.plugins.power org.gnome.settings-daemon.plugins.power button-power 'interactive' org.gnome.settings-daemon.plugins.power critical-battery-action 'nothing' org.gnome.settings-daemon.plugins.power percentage-low 1 org.gnome.settings-daemon.plugins.power priority 0 org.gnome.settings-daemon.plugins.power lid-close-suspend-with-external-monitor false org.gnome.settings-daemon.plugins.power idle-dim false org.gnome.settings-daemon.plugins.power button-hibernate 'hibernate' org.gnome.settings-daemon.plugins.power sleep-inactive-ac-type 'suspend' org.gnome.settings-daemon.plugins.power button-sleep 'suspend' org.gnome.settings-daemon.plugins.power button-suspend 'suspend' org.gnome.settings-daemon.plugins.power sleep-inactive-battery-timeout 0 org.gnome.settings-daemon.plugins.power time-low 1200 org.gnome.settings-daemon.plugins.power lid-close-ac-action 'nothing' org.gnome.settings-daemon.plugins.power notify-perhaps-recall true org.gnome.settings-daemon.plugins.power percentage-critical 1 org.gnome.settings-daemon.plugins.power percentage-action 1 org.gnome.settings-daemon.plugins.power sleep-inactive-battery-type 'suspend' org.gnome.settings-daemon.plugins.power time-action 120 org.gnome.settings-daemon.plugins.power lid-close-battery-action 'nothing' org.gnome.settings-daemon.plugins.power idle-brightness 30 org.gnome.settings-daemon.plugins.power sleep-inactive-ac-timeout 0 org.gnome.settings-daemon.plugins.power time-critical 300 org.gnome.settings-daemon.plugins.power active true org.gnome.settings-daemon.plugins.power use-time-for-policy false $ Elements order in a "for (… in …)" loop Does the "for…in" loop in Javascript loop through the hashtables/elements in the order they are declared? Is there a browser which doesn't do it in order? The object I wish to use will be declared once and will never be modified.  Suppose I have:  var myObject = { A: "Hello", B: "World" };   And I further use them in:  for (var item in myObject) alert(item + " : " + myObject[item]);   Can I expect 'A : "Hello"' to always come before 'B : "World"' in most decent browsers? Algorithm to detect overlapping periods The value of $\lim_{n \to \infty}\int_{0}^{1}nx^ne^{x^2}dx$ When I parent an object to follow a path and animate it, I only get a linear mode animation and changing that in Grapth Editor to bezier doesn't work! How to do that? When writing questions and answers here about the Harry Potter series, I often need a word for "someone who's not a Muggle". People often refer to "the wizarding world" as opposed to the Muggle word, so "wizard" would be one choice - but it seems slightly sexist to exclude witches in that way. On the other hand, "witch or wizard" is a bit cumbersome, much longer than the simple word "Muggle".  Is there a sensible word to use which is neither sexist nor cumbersome, that makes a good equivalent to "Muggle"? What would JK Rowling say to fill in a sentence such as this:     Muggles use technology, while [...] use magic. Converting Polygon into single or all Points using QGIS? Any nice, stable ways to keep a window 'Always on top' on the Mac? Why does factoring eliminate a hole in the limit? Apt sources.list problem , packages not found? I am trying to install WICD but getting following errors on my ubuntu 10.04 box  sudo apt-get install wicd   Err http://archive.ubuntu.schoolnet.lk/ubuntu/ lucid/universe python-wicd 1.7.0+ds1-2   Could not connect to archive.ubuntu.schoolnet.lk:80 (103.29.60.18). - connect (111: Connection refused) Err http://archive.ubuntu.schoolnet.lk/ubuntu/ lucid/main python-iniparse 0.3.1-1   Unable to connect to archive.ubuntu.schoolnet.lk:http: Err http://archive.ubuntu.schoolnet.lk/ubuntu/ lucid/universe wicd-daemon 1.7.0+ds1-2   Unable to connect to archive.ubuntu.schoolnet.lk:http: Err http://archive.ubuntu.schoolnet.lk/ubuntu/ lucid/universe wicd-gtk 1.7.0+ds1-2   Unable to connect to archive.ubuntu.schoolnet.lk:http: Err http://archive.ubuntu.schoolnet.lk/ubuntu/ lucid/universe wicd 1.7.0+ds1-2   Unable to connect to archive.ubuntu.schoolnet.lk:http: Failed to fetch http://archive.ubuntu.schoolnet.lk/ubuntu/pool/universe/w/wicd/python-wicd_1.7.0+ds1-2_all.deb  Could not connect to archive.ubuntu.schoolnet.lk:80 (103.29.60.18). - connect (111: Connection refused) Failed to fetch http://archive.ubuntu.schoolnet.lk/ubuntu/pool/main/p/python-iniparse/python-iniparse_0.3.1-1_all.deb  Unable to connect to archive.ubuntu.schoolnet.lk:http: Failed to fetch http://archive.ubuntu.schoolnet.lk/ubuntu/pool/universe/w/wicd/wicd-daemon_1.7.0+ds1-2_all.deb  Unable to connect to archive.ubuntu.schoolnet.lk:http: Failed to fetch http://archive.ubuntu.schoolnet.lk/ubuntu/pool/universe/w/wicd/wicd-gtk_1.7.0+ds1-2_all.deb  Unable to connect to archive.ubuntu.schoolnet.lk:http: Failed to fetch http://archive.ubuntu.schoolnet.lk/ubuntu/pool/universe/w/wicd/wicd_1.7.0+ds1-2_all.deb  Unable to connect to archive.ubuntu.schoolnet.lk:http: E: Unable to fetch some archives, maybe run apt-get update or try with --fix-missing? Integral of $\frac{1}{2x}$ How to add field history and product as a related list of opportunity in vf page I am trying the below code to add field history and product as a related list of opportunity in vf page, but its not working .  &lt;apex:relatedList list="OpportunityFieldHistory"/&gt; &lt;apex:relatedList list="Product"/&gt;   Can anyone tell me what is the correct way to write it.  Regards    Edit:  There are two Standard objects that have Opportunity history information,  and . The relatedList component works fine with a value of OpportunityHistories for the list attribute, but an error is thrown when using the value of Histories, even though the SObject describe information shows "Histories" as the child relationship name.   &lt;apex:relatedList list="OpportunityHistories"/&gt; &lt;!-- Works fine --&gt; &lt;apex:relatedList list="Histories"/&gt;            &lt;!-- Error --&gt; If $x$ and $y$ are irrational, is $x + y$ irrational? Is $x - y$ irrational? Let $H$ be a subgroup of $G$ with $[G:H]=n$ and $G$ finite.  Let $G$ act on left cosets of $H$ by left multiplication.  Let $N$ be the kernel of the action.  Show that $[G:N]$ divides $n!$.  Ok so I have a theorem that says that if $G$ is simple then it embeds into $S_n$.  So if $G$ is simple than I'm done because $G$ divides $n!$ and thus $N$ divides $n!$ and hence $[G:N]$ divides $n!$.  Now I also know that $N$ is the largest normal subgroup of $G$ contained in $H$.  Thus if $G$ isn't simple then it contains some non-trivial normal subgroup $K$ and thus $K\cap H$ is normal in $H$ and by the 2nd Iso Theorem $H/K\cap H\cong KH/H$...    As you can see I'm not sure where to go from here. I was hoping to prove that $K\cap H$ wasn't trivial and thus that $N$ couldn't be trivial since it must contain $K\cap H$, but I'm not sure I can, and even if I could I'm not sure that would help me in showing that $[G:N]$ is small enough to divide $n!$.  Can anyone give some guidance?  Thanks.