#odd speaks

[odds-anime]

Riyo is a lesbian. I strongly believe that statement.

[oddcabinboy]

Can you explain the maths behind SHOs?

I can certainly try!

I want to preface this by saying that I know regretfully little about physics, but I'll do my best. I'm assuming you're referring to Simple Harmonic Oscillators and not uhhh any other abbreviation it might stand for

because a SHM is periodic, we will be dealing with sines and cosines. unfortunately that's just the way of things. they're periodic functions (which I don't think comes as a surprise), and their derivatives come in especially handy.

we can use Hooke's law, it applies here or so I've been told. combining it with Newton's second law and rearranging terms a bit, we're left with -k/m y(t) = y''(t). to make it a little easier on the eyes, we define c=sqrt(k/m) such that we have y''(t) + c^2 y(t) = 0, lovely, she's beautiful.

she's also a second-order linear ODE (ordinary differential equation), which is an absolute mouthful but boils down to basically nothing. second-order refers to the highest derivative being y'', the second derivative of y, it's linear because the equation is in the form of a polynomial, and ordinary (which, rude) just means we're working with a single independent variable t (thank god)

how do we solve this, though? we use the exponential function! hurray! why? because it has a sick property, the derivative of e^x is e^x, riveting I know. let y=e^rt, then y''=r^2 e^rt, substituting and simplifying gives us something called the characteristic equation, r^2 + c^2=0, which can be factorized as (r+ci)(r-ci)=0, I hope you were hungry for imaginary numbers! so the roots here are r=+-ci, which tells us that the general solution to the ODE is given by

y(t) = a cos(ct) + b sin(ct) where a and b are arbitrary constants. (I hope you'll take my word for this. there is of course a reason why this is the general solution, but I feel like my answer is already long enough. it uses Euler's formula, trig identities and the fact that we're only interested in the real solutions, not the imaginary ones. physics is Real Life after all)

we aren't done! a general solution is.. too general. however, if we want to find what's called the particular solution, we need two initial conditions; the initial position, y(0) (so at t=0) and the velocity of the mass(?) which is y'(0), sick. let's see what this does.

y(0) = a cos(0) + b sin(0) = a (since cos(0)=1, sin(0)=0)

y'(0) = -ac sin(0) + bc cos(0) = bc, so b = y'(0)/c

thus, y(t) = y(0) cos(ct) + y'(0)/c sin(ct), awesome!

I've also seen the general solution written in the form A cos(ct-phi), I'm not entirely sure why, maybe to plot it? whatever the reason, this has to do with polar coordinates. (basically, if we're working on the real plane we use cartesian coordinates, x and y usually, polar coordinates are more commonly used in the complex plane. it's interesting for sure! but I don't know if it's particularly relevant)

I think this concludes this behemoth of a post, I really hope this is what you were looking for! if not.. at least I got to do some fun research

[odds-games]

I’m starting high school soon so I will be busy next month

[oddestoddish]

Of the Litten and Torracat we saved from the collector, there was one more that was adopted before we made the public listings.

Trick, a Zorua variant Litten, was taken in by a good friend of mine. A penpal from a different region. He sent me this picture of her today, and said she has a tendency to attack anything that wiggles. Including fingers, toes, and tails.

She’s a cutey, and she definitely fits my friend’s trickster personality. I’m glad she’s having fun in her new home.

[cuteteacakes]

NEW MUSE TIEM

Odd Strickland (name subject to change)

Librarian

All the book puns

How do you do, Fellow Kids?

Actually in his 30s

Trying his hardest to keep up with trends but dang it they’re going too fast!

Likes his tea, scone, and a good book

Basically me as a man hue U wU

[is-john-cis-today]

John Egbert is not boring.

It bothers me so much when people call John boring. Yeah I get it, John is THE GUY, the main character, the first person we’re introduced to and are supposed to be able to relate to, BUT that is not all he is. Everyone seemed to gravitate to the more “complex and angsty” characters like, for example, Dave. Don’t get me wrong, I actually really like Dave. He’s in my top three favorite homestuck kids.

I feel like because John was introduced as such a goof ball a lot of his more subtle character development is overlooked. John never cries during SBURB, he hardly even seems sad when he sees that his father is dead, just in shock. He uses his rant John Cusak, you know the one he made to Jade on his birthday on the ship, as a way to indirectly express his self loathing. John wants to be a good friend but he’s not always good at going deeper into things, especially himself. This isn’t because he doesn’t want to but it’s because he is afraid of the possible of the consequences and harsh realities they would reveal but at a certain point he just became unable to because he never developed the proper skills to do so.

John is just so much more that a “token cishet” or even just the “relatable male lead”. I just wish more of the fandom would actually look at him as more than a joke long enough to see that.

So yeah I really like John.

[odds-anime]

Lowk need a moot who will proof read my fics with me and help me with not making the characters ocish 🥹 🫰

[odds-anime]

How would we feel if I made a maki angst?