Balder W. Holst

Hello there!

My name is Balder and this is my personal website. Here i write down what i learn to maybe help others some day. For now i will just act like people are reading my articles, and make them for fun.

This website has three main sections:

I write these articles for fun, and even though i try to make sure that they are correct, i am not a perfect human and there are sure to be mistakes. Below is a list of most recent articles in all categories.

Recent Posts

Jævn Cirkelbevægelse
Jævn Cirkelbevægelse Jævn Cirkelbevægelse med lod Formel $$L=\frac{g}{4 \pi ^2 \cdot \cos(\theta)} \cdot T^2$$ $L$: Længden af snoren $T$: Perioden $\theta$: Vinklen fra lodret Vinklens indvirkning på perioden $$L=\frac{g}{4 \pi ^2 \cdot \cos(\theta)} \cdot T^2$$ $$\Updownarrow$$ $$\frac{1}{T^2}=\frac{g}{4 \pi ^2 \cdot \cos(\theta) \cdot L}$$ $$\Updownarrow$$ $$T^2={\frac{4 \pi ^2 \cdot L}{g}\cdot \cos(\theta)}$$ $$\Updownarrow$$ $$T=\sqrt{\frac{4 \pi ^2 \cdot L}{g}} \cdot \sqrt{cos(\theta)}$$ Kurvekørsel og Loop Vejsving uden hældning Bilen accelereres mod midten af cirkelbuen.
0001/01/01 · Notes
Karnaugh Map
Karnaugh Map (K-map) Alternative way of representing a truth table. Can be used to generate an expression from a truth table. It is easier than the Sum of Products method for large truth tables. Se slides: Lesson 3.pdf>page=30. The sides of a Karnaugh map “warp” around. The sides count in gray codes. Procedure Draw the biggest rectangles you can around the $1$’s. The amount of cells in each rectangle should be described by $2^k$.
0001/01/01 · Notes
KCL
Kirchhoff’s Current Law $$\sum I = 0 \s\text{towards every node}$$ “The current entering a node must equal the current exiting a node” If this was not true, charge would accumulate in some nodes, whilst being absent from others. Because of charge’s tendency to attract opposites imbalance evens out. Method Assign negative values to outgoing current, and positive to incoming. ex: $I_{in} + I_{in} - I_{out} = 0$
0001/01/01 · Notes
Keplers Lov
Keplers Lov $$\frac{T^{2}}{a^{2}}=k$$
0001/01/01 · Notes
Kinematrics
Kinematrics Mathematics for relating coordinate systems (frames), and calculating positions, angles and motions. All bodies are rigid and forces aren’t considered. Notes list from #kinematics sort file.name
0001/01/01 · Notes
Kinetisk Energi
Kinetisk Energi $$E_{kin}=\frac{1}{2} \cdot m \cdot v^2$$
0001/01/01 · Notes
Knudepunktsmetoden
Knudepunktsmetoden (Node-Voltage Analysis) Electrical Engineering Principles & Applications, Global Edition.pdf>page=82 Ide Opskriv alle knudepunkters KCL. Derfra kan strømme udledes. Til sidst kan spændinger udregnes med Ohm’s Lov. $$I_{A\rightarrow B}= \frac{v_A - v_B}{R}$$
0001/01/01 · Notes
Koblede Førsteordensdifferentialligninger
Koblede Førsteordens-differentialligninger Eksempel $$\frac{dy}{dt} = k_1x+k_2y$$ $$\frac{dx}{dt} = k_3x+k_4y$$ Differentierer $x$ i den første differentialligning $$x = \frac{1}{k_1} \frac{dy}{dt}-\frac{k_2}{k_1}$$ Vi differentierer med henhold til $x$ $$\frac{dx}{dt} = \frac{1}{k_1} \frac{d^2y}{dt^2}-\frac{k_2}{k_1}\frac{dy}{dt}$$ Indsæt $x$ og $\frac{dx}{dt}$ i ligning $2$. $$\frac{1}{k_1} \frac{d^2y}{dt^2}-\frac{k_2}{k_1}\frac{dy}{dt} = k_3\left(\frac{1}{k_1} \frac{dy}{dt}-\frac{k_2}{k_1}y \right) - k_4y$$ Simplificerer $$\frac{1}{k_1} \frac{d^2y}{dt^2} - \frac{dy}{dt} \left(\frac{k_2}{k_1} + \frac{k_3}{k_1} \right) + y\left(\frac{k_2 k_3}{k_1} +k_4\right) = 0$$ $$\Updownarrow$$ $$\frac{d^2y}{dt^2} - \frac{dy}{dt}(k_2+k_3) + y(k_2k_3+k_1k_4) = 0$$ Du kan det løses med denne formel.
0001/01/01 · Notes
Komplekse Tal
Komplekse Tal Calculus 9th.pdf>page=1083 $$w = a + ib, \s i^2 = -1$$ Her er $a$ og $b$ rigtige tal. Kan også skrives på >Polær Form BRUG ALDRIG $i = \sqrt{-1}$ SOM DEFINITION $$Re(w) = Re(a+ib)= a, \s Im(w) = Im(a+ib) = b$$ Intet $i$ i den imaginære del Tager udgangspunkt i Andengradspolynomier der har løsninger hvor diskriminanten er negativ. $$x = \frac{-b \pm i \sqrt{-d}}{2a}$$ Eksempel Dette er andengradsligninen $$2z^2 + 4z + 10 = 0$$ Dette er så diskriminanten $$d = b^2 - 4ac= -64$$ Altså er dette løsningen $$x = \frac{-b \pm i \sqrt{-(d)}}{2a} = -1 \pm 2i$$
0001/01/01 · Notes
Kondensator
Kondensator “Jo mere ladning, jo større spændingsforskel over pladen” “Man kan ikke afsætte effekt i en kondensator” - Jan Strømmen er nul når kondensatoren er opladt. Formler $$Q=C \cdot V_c$$ $C$ : Kapacitansen $\frac{\text{C}}{\text{v}}$. $Q$ : Ladning i kondensatoren. $V_c$ : Spænding over kondensatoren. Hvis man differentierer kan man finde strømmen. $$I_c = C \cdot \frac{dV_c}{dt}$$ $I_c$ : Strømmen gennem kondensatoren. Spænding kan derfor ikke ændre sig momentant, da det ville betyde en uendelig stor spænding.
0001/01/01 · Notes