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Impedance of Ultrasonic Sensor (UR1612MPR/UT1612MPR)

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I measured impedance of UR1612MPR/UT1612MPR with Analog Discovery 2. UR1612MPR is receiver and UT1612MPR is transmitter. Optimal frequency is 40kHz. UR1612MPR UT1612MPR

Template files' location in Autodesk Inventor 2023 and how to change default unit system

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location of template files C:\Users\Public\Documents\Autodesk\Inventor 2023 How to change default unit system for ipt file Open template file Go to Tools tab Click "Document settings" Go to Units tab

How to fix Maven blocking http repositories in macOS

1. Locate settings.xml https://stackoverflow.com/questions/3792842/where-is-mavens-settings-xml-located-on-mac-os 2. Modify settings.xml https://stackoverflow.com/questions/67001968/how-to-disable-maven-blocking-external-http-repositores

Printer Queue cleanup bat script for windows10

Following code clears printer queue. Please note that this script reboots your computer. net stop spooler del %systemroot%\System32\spool\printers\* /Q net start spooler SHUTDOWN -r -t 10

Derivation of Boltzmann distribution for 1-dimensional potential

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p(h):pressure n(h):number of particles in unit volume F(h):force applied to the each particle U(h):potential energy of the particle From equation of state, we obtain: \begin{equation} \label{eq:state} p(h)V=NRT \rightarrow p(h)=n(h)k_bT\tag{1} \end{equation} Considering equilibrium of forces in the gas between h and h+dh, we obtain: \begin{equation} Sp(h+dh)+n(h)F(h)Sdh=p(h)S\\ \rightarrow p(h+dh)+n(h)F(h)dh=p(h)\\ \rightarrow \frac{p(h+dh)-p(h)}{dh}=-n(h)F(h)\\ \rightarrow \frac{dp}{dh}=-n(h)F(h)\tag{2} \end{equation} By substituting (1) to (2),we can derive differential equation (3). \begin{equation} k_bT\frac{dn}{dh}=-n(h)F(h)\tag{3} \end{equation} ODE (3) can be solved by dividing both sides by n. \begin{equation} \frac{1}{n}\frac{dn}{dh}=-\frac{F(h)}{k_bT} \end{equation} Integrating both sides by h results in following. \begin{equation} \int \frac{1}{n}dn=-\frac{1}{k_bT} \int F(h) dh \end{equation} \begin{equation} \leftrightarrow \int \frac{1}{n}dn=-\frac{1}{k_b

mathjax test

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