Geometry And Divnity

Everyone who reblogs this will get a pick-me-up in their ask box.

Every. Single. One. Of. You.

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!

Computer simulations that teach themselves to walk.

A sand pendulum that creates a beautiful pattern only by its movement.

But  why does the ellipse change shape?

The pattern gets smaller because energy is not conserved (and in fact decreases) in the system. The mass in the pendulum gets smaller and the center of mass lowers as a function of time. Easy as that, an amazing pattern arises through the laws of physics.

We Need Your Help to Find STEVE

Glowing in mostly purple and green colors, a newly discovered celestial phenomenon is sparking the interest of scientists, photographers and astronauts. The display was initially discovered by a group of citizen scientists who took pictures of the unusual lights and playfully named them “Steve.”

When scientists got involved and learned more about these purples and greens, they wanted to keep the name as an homage to its initial name and citizen science discoverers. Now it is STEVE, short for Strong Thermal Emission Velocity Enhancement.

Credit: ©Megan Hoffman

STEVE occurs closer to the equator than where most aurora appear – for example, Southern Canada – in areas known as the sub-auroral zone. Because auroral activity in this zone is not well researched, studying STEVE will help scientists learn about the chemical and physical processes going on there. This helps us paint a better picture of how Earth’s magnetic fields function and interact with charged particles in space. Ultimately, scientists can use this information to better understand the space weather near Earth, which can interfere with satellites and communications signals.

Want to become a citizen scientist and help us learn more about STEVE? You can submit your photos to a citizen science project called Aurorasaurus, funded by NASA and the National Science Foundation. Aurorasaurus tracks appearances of auroras – and now STEVE – around the world through reports and photographs submitted via a mobile app and on aurorasaurus.org.

Here are six tips from what we have learned so far to help you spot STEVE:

1. STEVE is a very narrow arc, aligned East-West, and extends for hundreds or thousands of miles.

Credit: ©Megan Hoffman 

2. STEVE mostly emits light in purple hues. Sometimes the phenomenon is accompanied by a short-lived, rapidly evolving green picket fence structure (example below).

Credit: ©Megan Hoffman 

3. STEVE can last 20 minutes to an hour.

4. STEVE appears closer to the equator than where normal – often green – auroras appear. It appears approximately 5-10° further south in the Northern hemisphere. This means it could appear overhead at latitudes similar to Calgary, Canada. The phenomenon has been reported from the United Kingdom, Canada, Alaska, northern US states, and New Zealand.

5. STEVE has only been spotted so far in the presence of an aurora (but auroras often occur without STEVE). Scientists are investigating to learn more about how the two phenomena are connected. 

6. STEVE may only appear in certain seasons. It was not observed from October 2016 to February 2017. It also was not seen from October 2017 to February 2018.

Credit: ©Megan Hoffman 

STEVE (and aurora) sightings can be reported at www.aurorasaurus.org or with the Aurorasaurus free mobile apps on Android and iOS. Anyone can sign up, receive alerts, and submit reports for free.

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

Interesting submission rk1232! Thanks for the heads up! :D :D