differnetial equation

[tidal niche]

Have i drawn the diagram correct. Does the direction of the force change when the mass passes C

I cant seem to get the directions of all the forces correct

<@&791435371564892232>

[hidden fable]

The force is always towards C

When it’s extended it’s pushing back to C

When it’s compressed pushing out to C

And the resistive forces oppose motion

So taking away from C as positive, -4mx/9 - 4mv/3 + +4m/45 = ma so 9a + 12v + 4x=4/5

The minus on the first force is because our restoring force is always opposite direction to displacement x

And the minus on the second force is due to the velocity being towards the equilibrium so the resistive force is in the opposite direction to our velocity vector v

The key is x and v have encoded directions alr

[tidal niche]

Why aren’t both resistive forces in the same direction?

[tidal niche]

why does the third force also not have a minus on it

Is it because it’s a constant force that’s always acting in one direction

[hidden fable]

They are

[hidden fable]

Yes

It’s always in the positive direction

As I defined it

[hidden fable]

.

[hidden fable]

^

If velocity is left it’s -speed and —speed is +speed

[tidal niche]

is the equilibrium C?

im still tryna get my head round it

[tidal niche]

is this because the second force is directly proportional to v?

Is this diagram correct

Also is the equation of motion the same if the mass has just been released from B as it would be if its on the other side of C?

[tidal niche]

<@&791435371564892232>

im sorry to be a neusence

[hidden fable]

yh

[hidden fable]

well yh

but in the opposite direction

[hidden fable]

ye

we only want from B to A

[tidal niche]

so

just finding my working

is the diagram right?

and why is the 4m/45 not also negative?

@hidden fable

[hidden fable]

cus its got no vectors in

its just got constants

and its to the right

[tidal niche]

so is it like weight

[hidden fable]

no

its like friction

[tidal niche]

so weight always acts down

so

it always opposes motion

[hidden fable]

yes

thats the friction force

and the velocity resistance

[tidal niche]

but the other resistive force also does but because it has a vector in that makes it other way

[hidden fable]

yh

[tidal niche]

so is the resistive force with velocity always points the other way

[hidden fable]

resistive forces always do

[tidal niche]

yea but its doing the opposite of that because it has velocity in it?

[hidden fable]

nah

its still in that direction

[tidal niche]

so how can that be negative and the other force not be resistive force negative

[hidden fable]

because

velocity is to the left

which is the negative direction

so to make our force to the right

we put a negative infront of it

[tidal niche]

and we dont do that for the other resitive force because its a constant?

[hidden fable]

yes

[tidal niche]

this is raelly confusing me 😂

like im typing whats happening but its not going in

[tidal niche]

One last thing Is this diagram correct?

[hidden fable]

When it’s past C yes

[tidal niche]

so if its moving left and the force 4m/45 points right because its a resistive force why isnt it negative

just because its not a vector

[hidden fable]

Yh

[tidal niche]

when can this happen

just with friction

/ resistive forces

[hidden fable]

rlly depends

on what ur modelling

[jolly crater]

I’ll lyk next year once I’ve done fm g