help with a small expression regarding sin, cos, and tan.

[mortal marlin]

howdy, ok so i am studying physics and i have this this small thing i am trying to prove to my teacher... he is wrong a lot in math and many other things, he's too tired, we need to fix anything he writes, you cannot trust the things he writes on the board... nothing makes sense.

anywho, i have x(0) and v(0) you guys can call them x and v, the 0 is t=0 (at time zero)
so x(0) is x/dt and v(0) is v/dt and also v(o) is basically x/(dt^2)
v is a derivation of x based on time.

basically i am looking to express tan(phi)
v(0)/x(0) should be equal to tan(phi)
and so i had to build an equation to express v and x in a sin and cos way.
v = -omegaAsin(phi) (based on physics litterature)
x=Acos(phi) (based on physics litterature)

my question is this.
if i divide omegasin/cos, is the answer omega*tan or something else?

he says phi = atan(-omega*v/x)
i say phi = (atan(-v/x))/omega
gemini says atan(-v/omegax)

please help.. i'll send a screen shot of the math in an easier to read way thanks for everything..

[mortal marlin]

basically, is this right? if no, what is right?

[hushed remnant]

I mean, how are v and x depending on time?

You're missing a lot of context here.

[mortal marlin]

it's thier definition, graphs

placement over time

and velocity over time

that's why v(t)

and x(t)

[hushed remnant]

I'm not seeing the definition anywhere

[mortal marlin]

i just want at point (t=0)

[hushed remnant]

!original

[deft crow]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[mortal marlin]

am i allowed to take out -omega and just say the As disappear? and multiply minus omega times tan phi?

is a*tan(alpha) always equal to asin(alpha)/acos(alpha)

[hushed remnant]

I have no clue

context: M I S S I N G

[mortal marlin]

i just need general laws of mathematics on how sin cos and tan works, i'll figure the rest

[hushed remnant]

https://en.wikipedia.org/wiki/Trigonometric_functions

[mortal marlin]

i'll remake them so that's it's purely mathematic without physics.

x(t) --> f(x)
v(t) --> f'(x)
a(t) --> f''(x)

A=a
omega=b
phi=c

f(x) = acos(bx+c)
g(x)=f'(x)= -bacos(bx+c)
h(x)=f''(x)=-(b^2)acos(bx+c)

given that X = 0 in the graph.

express tan(c) and express c in any way you'd like using the f(x),f'(x), and lastly f''(x)

[mortal marlin]

it doesn't answer the specific question i have regarding multiplying sine or cosine with constants

[hushed remnant]

So, you are $\textit{given}$ that $x(t)=A\cos(\omega t+\phi)$ and are given $x(0)=0$ and you want to find $\phi$ purely in terms of $x$, $v$, and $a$?

[heady scarab]

SWR

[mortal marlin]

basically yeah

also you are given that v(0) = 0

[hushed remnant]

Then $x(t)=0$ for all $t$

[mortal marlin]

no

[heady scarab]

SWR

[mortal marlin]

cause t changed

[hushed remnant]

afraid so

[hushed remnant]

It's a consequence of differential equations

[mortal marlin]

if we input t=1

insted of t=0

we get a different thing

omega isn't 0, phi can be anything

[hushed remnant]

yeah but if you solve the constants such that x(0)=v(0)=0, then you can only get x(t)=0

[mortal marlin]

a(t) is 1.52 if that helps

when a(t) = 0 v(t) is max

[hushed remnant]

Okay, let's say $x(t)=A\cos(\omega t+\phi)$ and let's say $x(0)=0$. We $\textit{could}$ have $A=0$, but then we would have $x(t)=0$, and we are going to assume $x(t)\ne 0$, so we must have $A\ne 0$. So if $0=A\cos(\phi)$ and $A\ne 0$, then we can solve for $\phi$ and get $\phi=\frac{\pi}{2}$. However, this means $x(t)=A\sin(\omega t)$ and $v(t)=A\cos(\omega t)$, but this means $v(0)=A\cos(0)=A\ne 0$, which leads to a contradiction. Therefore, we cannot have $x(0)=v(0)=0$ and $A\ne 0$

[heady scarab]

SWR

[mortal marlin]

https://tenor.com/view/spring-constant-gif-18125173

this is basically the motion i am trying to describe

https://tenor.com/view/askey-happy-angry-spring-in-shm-gif-24835062

[hushed remnant]

simple harmonic motion

[mortal marlin]

yep

[hushed remnant]

I'm quite familiar with it

[mortal marlin]

that's awesome

[hushed remnant]

read this tho

[mortal marlin]

why can't we have no distance and no speed when we let go of an object

if i drop a ball from an 8 floor

x = 0
v = 0
a = max

let's say it was an egg

the moment before it goes boom.

we reached 0 and 0

and acceleration is max

they are all 3 the same formula, just derivitives of each other

if you'd like, i can give you numbers of anything except for phi

i did the experiment, i have data, i need the math to find if i have a phi or not

phi could be zero, and it could all be dependant on omega t

phi could be 42 also

here's the scenerio i'm explaining

[hushed remnant]

You $\textit{can}$ do $x=0$ if your coordinate system is relative to something else. But $x=A\cos(\omega t+\phi)$ describes displacement from the equilibrium point of a spring

[heady scarab]

SWR

[mortal marlin]

f=mg (gravity)
f=-kx (hook's law)
f=ma (2nd law of newton)

[hushed remnant]

And in such a case, you cannot have x(0)=v(0)=0 without also having x(t)=0

[mortal marlin]

correction, it describes displacement at time zero specifically x(0) which means it's Acos(phi)

A is 0.1 meters for example. that's how much i pulled before letting go

[hushed remnant]

No, I'm saying x(t) always describes displacement from the equilibrium point

[mortal marlin]

v(0) would be -omegaAsin(phi)

so that's
0.1cos(phi)
and 0.1sin(phi)

they aren't = 0 always

only at t=0

[hushed remnant]

You keep ignoring what I am trying to tell you though

[mortal marlin]

ok, i get that i don't get why it's an issue

[hushed remnant]

Just so I'm clear, you're still trying to assert that x(0)=v(0)=0 is possible without x(t) always being 0, right?

[mortal marlin]

yeah, cause if you made a graph using python with random data inside the formula, you still get sin and cos

it's not a linear flat line

which means you don't always get 0

[hushed remnant]

okay

[mortal marlin]

and you can see them both intercect at 0

v and x

[hushed remnant]

let's discuss this before we go further

[mortal marlin]

specifically

an object can have an independant speed.

right?

[hushed remnant]

$v(t)=A\omega\sin(\omega t+\phi)$, right?

[heady scarab]

SWR

[mortal marlin]

regardless of it's position

[mortal marlin]

minus

but yeah

[hushed remnant]

oh yeah minus.

okay, before I go further, let me say this..

[mortal marlin]

wait i think i understand now

[hushed remnant]

$x(0)=v(0)=0$ is possible if you do $x(t)=A\cos(\omega t+\phi)+x_0$ where $x_0$ is some non-zero constant.

[heady scarab]

SWR

[mortal marlin]

you say x(t) describes thingies from the center right? the equillibrium

[hushed remnant]

yes

[mortal marlin]

i never specifically mentioned that x=0 is equllibrium

x=0 is A

or anything else

you don't know that

[hushed remnant]

Hence where you would need this

[hushed remnant]

x=0 is A? What does that mean?

[mortal marlin]

let me explain for a moment

if i have a spring

and i pull it up, that's my max length right?

now because it's max length it'll ever be

it's also the opposite of the minimum length

it'll move from 10m to -10

or from 1 to -1

etc etc

[hushed remnant]

yup

[mortal marlin]

so my A (the height of cos and sin function) is x0

the moment i let go, that's the biggest heigt i'll ever have

[hushed remnant]

So that would be x(0)=A

[mortal marlin]

exactly

[hushed remnant]

not x(0)=0

[blissful iron]

I'm not sure how right I am, but in simple harmonic motion, the object oscillates between two specific points.
A function that's bounded only can be used for the equation of shm.
Tangent function's value goes from -infi to +infi.
How can tan be used here?

[mortal marlin]

it's a silly research thingy thingy, i am looking for math that will look like a graph in reallity not really looking for the actual formula, i am supposed to relearn and prove every thing from 0

been doing this since last year, god, i hate this part..

the plan is to get a general formula with tan and phi at the end

then make a python script with coefficeny and squared coefficency, and show that my math is technically right, and you can find simillarities with reallity and my constants etc..

it doesn't need to be 100% true or right, i just need to know to back up why everything i've made so far works the way it does

[mortal marlin]

thank you. i now finally get it

also sorry for being silly

[hushed remnant]

no worries

[blissful iron]

I see
But getting a general formula for shm with tan is kinda not possible?
It's periodic but it can basically never give you the output

Just because of the ranging

[mortal marlin]

i don't need the tan to be a physical dimention

i am using tan at the moment, cause i'll always have v and x

which means i can express phi

and always kind of theoretically know what extra angle was added to the general formula

[hushed remnant]

Anyway, if $x(0)=A$, then $\phi=0$

[mortal marlin]

yeah makes sense

[heady scarab]

SWR

[blissful iron]

ahhh
makes sense now

[mortal marlin]

i just need to show for now my teacher why this answer is right, and if not, then show him which answer is right and why etc.. (basing myself with math laws, no need for physics, i am just using my physics constants cause this is what i am trying to find, the value of phi inside my experiments with springs

[hushed remnant]

What are $x_0$ and $v_0$?

[mortal marlin]

ok, so we've established that x(0) isn't 0

[heady scarab]

SWR

[mortal marlin]

v(0) is zero. cause i want to start at the very top

[hushed remnant]

$x(0)$ $\textit{could}$ be zero, but then $v(0)\ne0$

[heady scarab]

SWR

[hushed remnant]

in the general case

[mortal marlin]

ik, i just specifically want to solve for when i started the experiment

which was with no velocity, the object being above it's equllibrium

[hushed remnant]

oh okay

then yes, $x(0)=A$ and $v(0)=0$

[heady scarab]

SWR

[mortal marlin]

i tried inserting values to see if it makes things simpler, and i am assuming my formula for phi is right.. how exactly would i solve this to figure out if i am right or not

here's the experiment's graph basically

y is sideways, ignore it. x is up and down, which is the graph on top

[hushed remnant]

Sorry but I'm still a little lost on what you are trying to do