GUI sway effect when moving the camera

Help and Feedback Scripting Support
#1

I have seen this in many games, when you are in first person, when you move your camera the scope has a like a bounce/sway effect. If you know how to achieve this please tell me.

Video of what I want to achieve:

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How do I make the UI move while the character is moving (Sway Effect)
#2

Using a sin wave or more commonly a spring (hookes law) are good ways to do this sway effect, essentially a player moves mouse to this position, instead of instantly snapping that position to that spot a scripter can use hooke’s law to first accelerate the movement (creating a easing effect) and then actually overshoot the intended position the player was trying to get at (this is good since players arent pixel perfect when aimming)

#3

Recreated this with motion blur as well:

local userInputService = game:GetService("UserInputService");
local runService = game:GetService("RunService");

local scopeFrame = (script.Parent:WaitForChild("Frame"));
local SCOPE_FRAME_POS = (scopeFrame.Position);

function Lerp(a, b, m)
	return a + (b - a) * m
end;

local swayX, swayY = 0, 0;
local SWAY_BLUR = Instance.new("BlurEffect");
SWAY_BLUR.Parent = workspace.CurrentCamera
SWAY_BLUR.Size = 0
local SWAY_SPEED = (5);
function RenderStep(dt)
	userInputService.MouseIconEnabled = false
	local delta = userInputService:GetMouseDelta();	
	swayX = Lerp(swayX, delta.X * 2, dt * SWAY_SPEED)
	swayY = Lerp(swayY, delta.Y * 2, dt * SWAY_SPEED)
	
	SWAY_BLUR.Size = Vector2.new(swayX, swayY).Magnitude
	scopeFrame.Position = SCOPE_FRAME_POS + UDim2.fromOffset(swayX, swayY)
end;

runService.RenderStepped:Connect(RenderStep)

Result:

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