The simple harmonic oscillator

Anonymous asked: Please explain the intuition of solving the SHM equation.

Okay Anon! Here you go, this is my rendition.

The problem

You have a mass suspended on a spring. We want to know where the mass will be at any instant of time.

Describe the motion of the mass

The physical solution

Now before we get on to the math, let us first visualize the motion by attaching a spray paint bottle as the mass.

Oh, wait that seems like a function that we are familiar with - The sinusoid.

Without even having to write down a single equation, we have found out the solution to our problem. The motion that is traced  by the mass is a sinusoid.

But what do I mean by a sinusoid ?

If you took the plotted paper and tried to create that function with the help of sum of polynomials i.e x, x2, x3 … Now you this what it would like :

By taking an infinite of these polynomial sums you get the function Since this series of polynomial occurs a lot, its given the name - sine.

I hope this shed some light on the intuition of the SHM equation. Have fun!

Tesla’s reply to his critics who balked at his idea of interplanetary communication and his explaination of his theory:

“Having no exact knowledge of the means of investigation used by other experimenters, I cannot judge of the value of their observations. I assume that the same circuit arrangements and devices have been employed which are described in patents and articles on Hertzian telegraphy. In these cases an aerial conductor, not directly connected with the ground, but separated from it by imperfect contacts or coils which prevent the passage of the current, receives the effects transmitted from a distance.

“The atmospheric disturbances in these arrangements, if I am to judge from my own experience, are so great that I have always doubted their practical value. In my investigations these disturbing atmospheric influences are almost wholly excluded. It would have been impossible for other experimenters to know the effects which I have discovered, for with the Hertzian devices only a very narrow region can be explored, where as I was able to observe the electrical condition of a large portion of the globe, a stretch of land 2,200 miles in width and breadth. That these actions are due to causes heretofore unknown I am convinced.

“I feel that I have not been led away by my imagination, but that my site was true as ever before, and I am confident that future investigation will confirm my statement.

“Nor have I the slightest doubt, judging from my experiments and measurements, that with a properly constructed electrical oscillator any amount of energy can be transmitted to a planet, as Venus or Mars, even at their greatest distance, sufficient to bring into action a sensitive instrument, such as I have been using in my own observations.

“Furthermore, it is an error to believe that a great expenditure of power is necessary for interplanetary communication. What is needed is an effect specifically great–an enormous rate of energy delivery, but lasting each time only a fraction of a second, so that the total power used up is small. Now, with my oscillator I can make this rate equal to five million horsepower and more, if necessary, and my calculations show that a small fraction of this rate is amply sufficient for conveying a message to Mars.

“Heretofore light was the only known agent for communicating with the planet. It is easy to show that by its means such a result is virtually impossible, owing to the rapid diminution of energy with the distance and the impossibility of concentrating in an instrument that energy falling upon a large area. By the method and machinery I have devised we are enabled to convey an immeasurably greater amount of energy to the planet, and the observer there, instead of utilizing in his instrument only an infinitesimal amount of the entire energy conveyed, can avail himself of a large portion of the same.

“A practical solution has thus been found both for transmitting and receiving messages, and we can only hope that there are beings as far as advanced, and possibly further than we are ourselves. I see no harm in holding fast to this possibility. This thought cannot but make us better and give us a fresh interest in life.“

–Nikola Tesla

“Tesla Confident Of Speaking Mars.” New York Herald, January 6, 1901.


If you put that ball on that machine while it wasn’t spinning, it would just roll straight down the lower sides. 

The raised edges would keep it in the middle line, but it’s only controlled in one direction. By spinning it, you constantly alternate the position of the tall sides, meaning that the ball is held in the middle, never able to fall off.

Particle accelerators control particles in the same way. Magnetic or electric fields can only direct particles in one plane at a time, so to keep a beam of particles rushing down a particle accelerator in one focused stream, the current gradient must constantly oscillate. This means the particles are constantly held in place, never able to shoot off in one direction.

Here’s the same principle in action: these are tiny pollen grains being held in place by an oscillating field. Rods in the four corners of the beam establish a field that oscillates many times a second to keep the pollen trapped. If it didn’t constantly switch, the pollen would all fly off in one direction.

Watch the full film with Dr Suzie Sheehy for more.

i feel like gatiss and moffatt didn’t really get what they signed up for like…. they should have realised that if you’re going to write a sherlock holmes adaptation, then you’re naturally going to attract fans who can be counted on to pull apart every tiny detail of a show. every word that the writers will say about it, every little tiny bit of info we are provided with, we’re gonna use them to theorise.

LIKE: if you tell us ‘it’s a love story,’ and have always dreamed of the day when a tv show will have a gay detective and his boyfriend and be considered completely normal, and if you tell us that he’s a man out of his time, and if you tell us to ‘be part of making history,’ and if we are told ‘oscillation on the pavement always means there’s a love affair,’ and that ‘neither of us were the first you know’………………………….there are literally too many examples to even fit into one post but like, come on??!?!?!!! we deserved better 

Let's talk about cusps!!

Cusps, or cusp signs, are these really kick ass people who are born at the very end and very beginning of their sign month. Here’s how it goes for those who don’t know. I’ll go ahead and add in my own opinion of them since I am one and that seems to be how these things go xD

Aries-Taurus: AKA the Cusp of Power- April 19th  to April 24th    Y'all are just cool beans. Seems like you got all the good traits of both Aries and Taurus. You’re loving and compassionate, but hardworking as fuck. It’s really refreshing actually.

Taurus-Gemini: AKA the Cusp of Energy- May 19th  to May 24th        I don’t know much about you guys, but I’ve only met a handful of you and I really like talking to y'all on an intellectual level. You have a tendency to be FREAKISHLY smart. Always testing the smarty pants animal on those stupid animal quizzes that they force you to take in school. Also you’re super sweet to those you know. I have one really good friend who is a Taurus/Gemini cusp and she’s the type of person who like… talks to people in line at the supermarket if she’s in the right mood since Geminis tend to be really friendly, but Taurus’ are pretty introverted so they have to be in the right mood to do it, ya know?

Gemini-Cancer: AKA the Cusp of Magic- June 19th  to June 23rd YOU!!! ARE!!!! SO!!!! CUTE!!!!! My god you’re literally the epitome of adorable and shy and creative and its just. yeah. You make the best art in the world and I’m always so excited when you get excited about something you made because its just… contagious excitement. They get over things a lot faster than Cancers do which is nice, but they’re more homebodied than Geminis which, as an Aquarius/Pisces cusp (I get along best with this sign, couldn’t you tell?) is kind of annoying at times because they wanna stay home more than not, but they’re good parents??? So it works.

Cancer-Leo: AKA the Cusp of Oscillation- July 19th  to July 24th    You know… I was always kind of confused about the definition of this cusp?? Like… oscilation…. what the fuck kind of cusp is an oscillation??? Well…. a cancer/leo cusp is a good way to explain it. Personally, I’m terrified of these cusps. My cusp and this cusp DO NOT get along very well because I’m a very shy, easily frightened person and this cusp is basically a Leo on fucking steroids. They get angry a lot, but they’re angry in like…. a prideful way???? I don’t really know how to explain it. Just. Don’t get on their bad side. From what people say though, they are really caring and extremely passionate. They make crazy good politicians and lawyers and like… powerful debating people.

Leo-Virgo: AKA the Cusp of Exposure- August 19th to August 24th Hi. This cusp confuses the ever loving shit out of me. Like.. Really a lot. They’re the most introverted extroverts I’ve ever met in my life and I never know what to do with them??? You’re all like “Let’s go out!!! And!!! Read this book in the corner because I’m tired of being out and about……” Um…. what? You love having fun, and you love expressing your feelings once you’re comfortable, but you never quite have a grasp on the exact way to do it and sometimes that really bothers you. Oh. And you REALLY. Don’t like being criticized. Like… at all. Somehow I’m friends with the most of you though so who knows.

Virgo-Libra: AKA the Cusp of Beauty- September 19th  to September 24th     I’ve only met like.. two of you, and you’re so freakin chill I never know what to do around you, but apparently you worry a lot from what I’ve read. You don’t show it though. Also, you’re actually really pretty I promise. Virgo/Libra can either be super cocky about their looks or super modest. I’m sorry this is so short Dx

Libra-Scorpio: AKA the Cusp of Drama and Criticism- October 19th  to October 24th   So I’ve never met a Libra/Scorpio cusp now that I think of it. So this is totally off of a search of things I found. Bear with me.– APPARENTLY. 1. y'all are really freakishly pretty. 2. y'all are really cool, but you don’t give up information very easily so there’s that. and 3. You really like love, but you also have a tendency to be super serious at times (not as broody as Scorpios though)

Scorpio-Sagittarius: AKA the Cusp of Revolution- November 19th  to November 24th    The epitome of the “indie hipster” cusp. They’re suuuuuuper creative. Really arty people. Tend to have a LOT of things to say about a LOT of different things which sounds like everyone, but them more than ‘normal’ I guess? I don’t really know how to explain it. These cusps are the ones that are most likely in my opinion to go into like…. journalism or like… political activism because of how wordy and creative they are. They can be really nice too if you’re on their good side but if you’re not they can destroy you from the inside out so be careful.

Sagittarius-Capricorn: AKA the Cusp of Prophecy- December 19th to December 24th    My dad is one of these!!! They’re kind of weird, but winter signs tend to get along better than the other signs so its okay xP THEY! ARE! SO! FUNNY! A lot of people don’t understand their humor though which I find really sad, but if you live with them for a while or are around them and you understand their humor and such, they’re freakin hilarious. They keep their emotions bottled, and they stay pretty happy around people they just met. They don’t like to admit to weakness either. Like…. ever. At all. They love with their entire heart, and if they aren’t feeling it, they’ll tell you if they don’t like you.

Capricorn-Aquarius: AKA the Cusp of Mystery and Imagination- January 15th  to Jan 22nd   So these people scare me. Ever had those people who just like… omit an aura of power around you? Yeah that’s a Capricorn/Aquarius. They really do scare me, but apparently they make really good actors because there’s a ton of them in Hollywood. They’re crazy good at whatever they do. Most of the time they test into the like…. flamboyant or 'party animal’ type on the aforementioned middle school animal tests.

Aquarius-Pisces: AKA the Cusp of Sensitivity- February 18th  to February 22nd    This is me!!! I am this!!! Hi!!! So we have a tendency to be freakishly creative, but really sensitive and that’s why. I don’t know if all Aquarius/Pisces cusps are like this, but I’m really really attention deficit and energetic which makes us come off as dismissive or frustrated. We do well in positions of leadership and control, but we have to do things our own way. Doing things someone else’s way is REALLY NOT OKAY with someone in this cusp. Most of the time because we’ve already thought through the most logical way to do it and saw that your way is wrong. We’re freakishly smart too, we just don’t like to show it. :P 

Pisces-Aries: AKA the Cusp of Rebirth- March 19th  to March 26th     So from what I’ve gathered, which isn't very much so bear with me…. but from what I’ve gathered you like your alone time, but you also REALLY like to party when you’re in the mood for it. Like you won’t go down without a fight if you wanna party and someone tells you no. I think that’s the Aries part? Like…. you get freakishly passionate about the things you do which comes very strongly from both sides. But then its HOW you do them that’s very much Aries-esque. Like…. I dunno how to really explain it well, but you’re very aggressive lovers, and you fight with your whole body. And yeah. There isn’t much of a better way to explain it than that. I’d say you need to chill, but I feel like if you tried to chill you'd just get really depressed and a depressed Aries is like the freakin end of the world and no one wants that. 

So yeah. Cusps are really cool. A lot of people don’t know they’re cusps. A lot of people don’t know anything about cusps. But cusps have a tendency to be about ten times stronger spiritually, but about ten times weirder when compared to the average sign. So there’s that. It’s really cool and this post is going to get super duper long if I go on about them. So I’m going to stop while I’m ahead even though this post is already like a million miles long. I hope this helps anyne who has asked me about cusps??

I edited a couple things in here so that they’d be a bit more accurate. I reread a handful after it started to gain a couple notes and realized some of the little excerpt thingies sounded like I was ragging on the cusps a little.

Lin-Manuel Miranda is basically asking us out to dance with his new salsa mixtape

Click through to listen and click here for Lin’s annotations!

It’s no surprise that Lin-Manuel Miranda is a music lover. We can witness his meticulous care and respect for music oscillating from his Broadway-musical hits to singing and writing songs for movies. Now, Lin Manuel has elegantly curated a star-studded mixtape on his Spotify account. He calls it “I relish your wit! I SALSA YOUR FACE.” The mixtape features classics from salsa legends such as Celia Cruz and Willie Colón. Lin-Manuel Miranda proudly accentuates the beauty of salsa and the culture it is derived from.

More than music, Lin-Manuel is offering us a history lesson. Music is a portrait of culture, and it falls within the framework of oral tradition. Songs provide us with a socio-political landscape of society. Hence, music is an educational tool;  it may be used to create awareness, provide knowledge of the past, and a map of where we are heading.

Lin-Manuel Miranda showcases a wide selection of salsa songs. More than percussions and rhythm sections – it’s the importance behind salsa and its identity. Salsa is beautifully anchored in voices of immigrants, the sound of the combined stories and miles travelled from home. Beyond a genre or rhythm, salsa is the quintessential sum of latinx experiences.