How does a Cloak of Displacement interact with a tortle’s Shell Defense?

The cloak has a property that causes creatures to have disadvantage on attack rolls against the one wearing it, and

This property is suppressed while you are incapacitated, restrained, or otherwise unable to move (DMG, pg 158).

The way Shell Defense is described

You can withdraw into your shell as an action… While in your shell, you are prone, your speed is 0 and can’t increase, you have disadvantage on Dexterity saving throws, you can’t take reactions, and the only action you can take is a bonus action to emerge from your shell (EGW, pg 181).

is effectively the same as being both incapacitated and restrained, with the only notable difference being that an attack against a prone creature

has advantage if the attacker is within 5 feet of the creature. Otherwise, the attack roll has disadvantage (PHB, pg 292).

While extremely similar mechanically, the tortle using Shell Defense is technically neither restrained nor incapacitated. Furthermore, the ability to emerge from its shell as a bonus action implies the capacity to then move during that turn if the tortle chooses to, so neither are they otherwise unable to move.

As such, would the Cloak of Displacement work for a tortle using Shell Defense (and thus cancel out the advantage melee attackers would normally have due to the prone condition)?

RAW and RAI interpretations are both desired.

Is there a way for a Hex Channeler Witch to gain access to the Displacement spell?

Is there a way for a Witch with the Hex Channeler archetype to have Displacement on her spell list?

For my purpose, I’m dealing with an NPC. I can make changes to the Witch Patron, Feats, Skills, and Archetypes (as long as she retains the Hex Channeler’s ability to channel negative energy offensively). However, I can’t change the NPC’s gear much – if the PCs kill her, they’ll get enough gear without adding a Ring of Spell Storing on top of everything else.

While I could just give a witch the spell via GM fiat, I don’t want to in this case. My players are very interested in character builds and are likely to ask how the NPC worked. Since one or more PCs might die in the fight, I’d prefer to avoid answering "it’s not really possible".

1D Wave Equation: Vertical Rod and Displacement vs. Textbook Solution

I am trying to setup Mathematica to analyze a vertical round rod under its own weight, fixed on one end free on the other. I have the 1D wave equation and a distributed load to represent the self weight of the round rod.

Vertical Rod Layout

The problem is when I compare the Mathematica solution to the textbook solution the two do not agree.

Sample problem is given below.

Y = 199*^9; (*Young's modulus in Pa *) \[Rho] = 7860; (* Steel density in kg/m^3*) dia = 1/39.37; (* 1" dia converted to meters*) c = Sqrt[Y/\[Rho]]; len = 1000; (*length in meters*) tmax = 5; (* Max time for analysis*) area = \[Pi]*dia^2/4; (*Round rod cross sectional area*) wtfactor = \[Rho]*9.81*area/len;  frwt[x_] := \[Rho]*    area*9.81*(1 -       x/len); (*Rod Self weight imposed as a distributed load*) nsol6 = NDSolve[{\!\( \*SubscriptBox[\(\[PartialD]\), \({t, 2}\)]\(z[x, t]\)\) == c^2*\!\( \*SubscriptBox[\(\[PartialD]\), \({x, 2}\)]\(z[x, t]\)\) + frwt[x] +       NeumannValue[0, x == len],    z[0, t] == 0}, z[x, t], {x, 0, len}, {t, 0, tmax},   Method -> {"FiniteElement",      "MeshOptions" -> {"MaxCellMeasure" -> 10}}   ] fnnsol6[x_, t_] = nsol6[[1, 1, 2]] Plot3D[fnnsol6[x, t], {x, 0, len}, {t, 0, tmax},   PlotLabels -> Automatic, AxesLabel -> Automatic]  deltaL = ((\[Rho]*9.81*len^2)/(  Y*2)) (*Textbook elongation for a vertical rod under self weight*) calcdeltaL =   fnnsol6[len,    5] (*Calculated delta Length from PDE solution.  Should match \ textbook*)  deltaLfunc[x_, l_] := \[Rho]*9.81*   x*(2*len - x)/(2*Y) (*Verified Correct*) xydata = Thread[{Range[0, 1000, 100],      deltaLfunc[x, 1] /. {x -> Range[0, 1000, 100]}}]; xydata2 =   Thread[{Range[0, 1000, 100],     Reverse[a]}]; (*Same answer different calc format for debugging*) Show[Plot[fnnsol6[x, 0], {x, 0, len}, PlotLabels -> {"PDE Val"},    PlotRange -> All   ],  ListLinePlot[xydata2, PlotStyle -> Green, PlotLabels -> {"Correct"}]] 

If you’ve read this far, thank you.

In summary my question is: Is this a Mathematica issue or a PDE setup problem? The PDE is right out of a textbook so I don’t think that’s the problem but Mathematica gives no errors and I am out of troubleshooting ideas so looking for some help.

Thank You

Convert Cloak of Displacement to a static bonus instead of disadvantage

One of my players has a Cloack of Displacement, which grants, for every round, monsters have disadvantage attacks against the player until the first attack hits.

What follows from that power, is that I have to ask the player for every attack, if the monster has disadvantage or not. That is an extra effort I don’t want to do; the information about whether or not he has a benefit is on his side of the table. (Note: as a DM I always ask “does AC X hit you?”)

So, we want to change the Cloak; instead of granting the monster disadvantage on their attack, the Cloak offers him, for every round, a bonus to AC, until he is hit.

Here is my question; what bonus should the Cloak give to the player?

Assume the player is a level 12 PC with an AC of 16. If we need to take the attack bonus of the monsters into account; assume a master needs to roll a 10 to hit.

Does Cloak of Displacement hide your character’s location or do others see two bodies?

Description for Cloak of Displacement (emphasis mine):

While you wear this cloak, it projects an Illusion that makes you appear to be standing in a place near your actual location, causing any creature to have disadvantage on Attack rolls against you. If you take damage, the property ceases to function until the start of your next turn. This property is suppressed while you are Incapacitated, Restrained, or otherwise unable to move.

Does that mean the cloak makes your actual body unable to be seen and projects an illusion of your body nearby, or are both bodies visible?

Calculate initial velocity based on displacement, time and constant acceleration.

“A car has a constant speed along a road. It goes down a hill at a constant acceleration. 50s after it goes down the hill the speed is doubled and 50s later it reaches the end of the 200m hill and is back at a constant speed. Find out the initial velocity and acceleration.”

At first I made relevant graphs to see if I could find some useful information from that but no luck. Then I tried to use the “suvat” equations but we haven’t learned them in class so I’m not allowed to use them, which is why I’m stuck as to how to solve this basic problem.