oscilator

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!

The inventor, whose 700 basic patents include widely used methods of large-scale distribution of electricity, assumed on his 78th birthday the aspect of a sinister wizard, when he confessed that in his bony, wedge-shaped head started the Houston street earthquake of 37 years ago.

One day violent tremors shock a neighborhood. They centered mysteriously, in one building. People were thrown into panic. Firemen and police responded to alarms.

Suddenly the vibrations stopped. Tesla said the “quake” ceased when he snatched up a hammer and knocked a gadget from the wall of his laboratory. His workshop then was in the most affected building. Where it is now he refused to reveal.

The gadget he said, was a vibration amplifying mechanism set to harmonise with the building’s vibrations. He said a small quake maker could shake a whole city to pieces.

“Has Invented Machine That Can Start Real Earthquake.” Zanesville Signal, Zanesville, Ohio, July 12, 1935.

Voyager: The Space Between

Our Voyager 1 spacecraft officially became the first human-made object to venture into interstellar space in 2012. 

Whether and when our Voyager 1 spacecraft broke through to interstellar space, the space between stars, has been a thorny issue. 

In 2012, claims surfaced every few months that Voyager 1 had “left our solar system.” Why had the Voyager team held off from saying the craft reached interstellar space until 2013?

Basically, the team needed more data on plasma, which is an ionozied gas that exists throughout space. (The glob of neon in a storefront sign is an example of plasma).

Plasma is the most important marker that distinguishes whether Voyager 1 is inside the solar bubble, known as the heliosphere.  The heliosphere is defined by the constant stream of plasma that flows outward from our Sun – until it meets the boundary of interstellar space, which contains plasma from other sources.

Adding to the challenge: they didn’t know how they’d be able to detect it.

No one has been to interstellar space before, so it’s  like traveling with guidebooks that are incomplete.

Additionally, Voyager 1’s plasma instrument, which measures the density, temperature and speed of plasma, stopped working in 1980, right after its last planetary flyby.

When Voyager 1 detected the pressure of interstellar space on our heliosphere in 2004, the science team didn’t have the instrument that would provide the most direct measurements of plasma. 

Voyager 1 Trajectory

Instead, they focused on the direction of the magnetic field as a proxy for source of the plasma. Since solar plasma carries the magnetic field lines emanating from the Sun and interstellar plasma carries interstellar magnetic field lines, the directions of the solar and interstellar magnetic fields were expected to differ.

Voyager 2 Trajectory

In May 2012, the number of galactic cosmic rays made its first significant jump, while some of the inside particles made their first significant dip. The pace of change quickened dramatically on July 28, 2012. After five days, the intensities returned to what they had been. This was the first taste test of a new region, and at the time Voyager scientists thought the spacecraft might have briefly touched the edge of interstellar space.

By Aug. 25, when, as we now know, Voyager 1 entered this new region for good, all the lower-energy particles from inside zipped away. Some inside particles dropped by more than a factor of 1,000 compared to 2004. However, subsequent analysis of the magnetic field data revealed that even though the magnetic field strength jumped by 60% at the boundary, the direction changed less than 2 degrees. This suggested that Voyager 1 had not left the solar magnetic field and had only entered a new region, still inside our solar bubble, that had been depleted of inside particles.

Then, in April 2013, scientists got another piece of the puzzle by chance. For the first eight years of exploring the heliosheath, which is the outer layer of the heliosphere, Voyager’s plasma wave instrument had heard nothing. But the plasma wave science team had observed bursts of radio waves in 1983 and 1984 and again in 1992 and 1993. They determined these bursts were produced by the interstellar plasma when a large outburst of solar material would plow into it and cause it to oscillate.

It took about 400 days for such solar outbursts to reach interstellar space, leading to an estimated distance of 117 to 177 AU (117 to 177 times the distance from the Sun to the Earth) to the heliopause.

Then on April 9, 2013, it happened: Voyager 1’s plasma wave instrument picked up local plasma oscillations. Scientists think they probably stemmed from a burst of solar activity from a year before. The oscillations increased in pitch through May 22 and indicated that Voyager was moving into an increasingly dense region of plasma.

The above soundtrack reproduces the amplitude and frequency of the plasma waves as “heard” by Voyager 1. The waves detected by the instrument antennas can be simply amplified and played through a speaker. These frequencies are within the range heard by human ears.

When they extrapolated back, they deduced that Voyager had first encountered this dense interstellar plasma in Aug. 2012, consistent with the sharp boundaries in the charged particle and magnetic field data on Aug. 25.

In the end, there was general agreement that Voyager 1 was indeed outside in interstellar space, but that location comes with some disclaimers. They determined the spacecraft is in a mixed transitional region of interstellar space. We don’t know when it will reach interstellar space free from the influence of our solar bubble.

Voyager 1, which is working with a finite power supply, has enough electrical power to keep operating the fields and particles science instruments through at least 2020, which will make 43 years of continual operation.

Voyager 1 will continue sending engineering data for a few more years after the last science instrument is turned off, but after that it will be sailing on as a silent ambassador. 

In about 40,000 years, it will be closer to the star AC +79 3888 than our own Sun.

And for the rest of time, Voyager 1 will continue orbiting around the heart of the Milky Way galaxy, with our Sun but a tiny point of light among many.

Make sure to follow us on Tumblr for your regular dose of space: http://nasa.tumblr.com.

Date a trickster who only speaks directly to crows, coyotes, and you. A trickster who regifts the offerings from their followers to children, distributed by need and potential for mischief. Who originated the alignment Chaotic Good. Who will repair your serpentine belt for free but rearrange the stations on your radio presets for the fun of it. Who says I love you with a serenade, composed and played on the rattle of 17 oscillating fans. Who thinks gender is the punchline to a joke they misheard. Who makes you fancy coffee and reminds you to give ‘em hell every morning.

the night shift (m.)

;pairing — hoseok/reader

;summary — working the graveyard shift means you’re exhausted by the time 9am comes around. lucky for you, 9am happens to be your neighbors’ favorite time for obnoxious sex. lucky for them, you’re always up for a challenge. shitty neighbors don’t always have to be a bad thing.

;warnings — language | mild unintentional voyeurism/mentions of exhibitionism | slight instances of jealousy | unprotected sex | oral sex | face-sitting | mentions of masturbation | very mild cumplay | soft dom/sub tones

;word count — 11k

;a/n — this wasn’t the hoseok story i originally wanted to post this week but this idea really excited me. happy hixtape season, everyone!

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huei-doodles  asked:

hello! idk if i've ever sent you this message before, but i was scrolling thru ur blog just now, and i wanted to say that your stuff is very pretty! your style is so cute, and artistic! <3

As you can see, opinions are divided but thank you

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.