## Mechanical Waves

Waves.  The wave speed $v=\lambda f$, $\lambda$ – the wavelength, $f$ – the frequency.

Wave functions and wave dynamics.  The displacement of individual particles in the medium
$y(x,t)=A\cos[\omega(\frac xv-t)]$ (or, more intuitively, $y(x,t)=A\cos[\omega(t-\frac xv)]$)
$y(x,t)=A\cos2\pi(\frac x\lambda-\frac tT)$
$y(x,t)=A\cos(kx-\omega t)$, where $k=\frac{2\pi}\lambda$ and $\omega=2\pi f=vk$
Wave function: $\frac{\partial^2y(x,t)}{\partial x^2}=\frac1{v^2}\frac{\partial^2y(x,t)}{\partial t^2}$

## How to Remove Git History

1. Checkout
git checkout --orphan latest_branch
git add -A
3. Commit the changes
git commit -am "commit message"
4. Delete the branch
git branch -D master
5. Rename the current branch to master
git branch -m master
6. Finally, force update your repository
git push -f origin master

## Alternating Current

Voltage, current, and phase angle.  In general, the instantaneous voltage $v=V\cos(\omega t+\phi)$ between two points in an ac circuit is not in phase with the instantaneous current $i=I\cos\omega t$ passing through those points.

Resistance and reactance.  The voltage across a resistor is in phase with the current, $V_R=IR$.  The voltage across an inductor leads the the current by $\frac\pi 2$, $V_L=IX_L$, inductive reactance $X_L=\omega L$.  The voltage across a capacitor lags the the current by $\frac\pi 2$, $V_C=IX_C$, capacitive reactance $X_C=\frac1{\omega C}$.

Impedance and the L-R-C series circuit.  In general ac circuit, the voltage and current amplitutes are related by the circuit impedance $Z$, $V=IZ$.  In an L-R-C series circuit, $Z=\sqrt{R^2+(\omega L-\frac1{\omega C})^2}$, $\tan\phi=\frac{\omega L-\frac1{\omega C}}R$.

Power in ac circuits.  The average power input to an ac circuit: $P_{av}=\frac12VI\cos\phi=V_{\mathrm{rms}}I_{\mathrm{rms}}\cos\phi$, where $\phi$ is the phase angle of the voltage relative to the current.  The factor $\cos\phi$ is called the power factor of the circuit.

Resonance angular frequencey.  $\omega_0=\frac1{\sqrt{LC}}$.

Transformers.  $\frac{V_2}{V_1}=\frac{N_2}{N_1}$, $V_1I_1=V_2I_2$.

## Mutual Inductance

Mutual inductance.  When a changing current $i_1$ in one circuit causes a changing magnetic flux in a second circuit, an emf $\mathcal{E}_2$ is induced in the second circuit.  $\mathcal{E}_2=-M\frac{di_1}{dt}$ and $\mathcal{E}_1=-M\frac{di_2}{dt}$, $M=\frac{N_2\Phi_{B2}}{i_1}=\frac{N_1\Phi_{B1}}{i_2}$ – mutual inductance, $N_1$ – number of turns of coil of the first circuit, $\Phi_1$ – average magnetic flux through each turn of coil 1.

Self-inductance.  A changing current $i$ in any circuit causes a self-induced emf $\mathcal{E}=-L\frac{di}{dt}$$L=\frac{N\Phi_B}i$ – depends on the geometry of the circuit and the material surrounding it.

Magnetic field energy.  An inductor with inductance $L$ carrying current $I$ has energy $U$ associated with the inductor’s magnetic field: $U=\frac12LI^2$.  Magnetic energy density: $u=\frac{B^2}{2\mu}$.

R-L circuits.  In an R-L circuit the growth and decay of current are exponential with time constant $\tau=\frac LR$.

L-C circuits.  An L-C circuit undergoes electrical oscillations with an angular frequency $\omega=\sqrt{\frac1{LC}}$.

L-R-C circuits.  The frequency of damped oscillations $\omega'=\sqrt{\frac1{LC}-\frac{R^2}{4L^2}}$.

## Oscillation of a Mass-Spring System Compared with Electrical Oscillation in an L-C Circuit

### Mass-Spring System

• Kinetic energy = $\frac12mv_x^2$
• Potential energy = $\frac12kx^2$
• $\frac12mv_x^2+\frac12kx^2=\frac12kA^2$
• $v_x = \pm\sqrt{\frac km}\sqrt{A^2-x^2}$
• $v_x=\frac{dx}{dt}$
• $\omega=\sqrt{\frac km}$
• $x=A\cos(\omega t+\phi)$

### Inductor-Capacitor Circuit

• Magnetic energy = $\frac12Li^2$
• Electrical energy = $\frac{q^2}{2C}$
• $\frac12Li^2+\frac{q^2}{2C}=\frac{Q}{2C}$
• $i = \pm\sqrt{\frac1{LC}}\sqrt{Q^2-q^2}$
• $i=\frac{dq}{dt}$
• $\omega=\sqrt{\frac1{LC}}$
• $q=Q\cos(\omega t+\phi)$

## Uncharted 4: A Thief’s End

Surprisingly awesome!

No proverbial zombies or substances this time.  Deeper and more likeable characters, who you actually care about – nothing like “The Last of Us” with its intrusive “emotional bond development” crap.  Way better from moral standpoint.  A lot (a lot!) of details.  Very impressive facial expressions.  A real treat for vehicle driving fans.  Incredibly small number of bugs.  I didn’t feel irritated with the gamepad while shooting (like I did playing Uncharted 1-3).

The biggest con I can think of is the traditional (for the Uncharted series) total lack of (perceived) cooperation among opposing NPCs.  Of course, if one of the NPCs sees you, a bunch of others will attack you as well, but they won’t say anything – as if they just communicate telepathically.  Probably a design choice, because there’s already a lot of comments and remarks going on between the player and his allies.

Also, I didn’t particularly like the two ending scenes.  The thing is, all the three Drakes – who we meet in the game (Elena is somehow sill Fischer) – lie to each other, to Elena, and to others, at one point of the game or another.  And only Nathan has to pay for it, and only a little.  And the only guy in the whole game who is actively, seriously not happy about lying is… the villain!  Who dies in a deus-ex-machina way – as usual in the Uncharted series.

P.S. How come Rafe didn’t see Sam at Rossi???

P.P.S. Actually, that’s not the only curious thing about the game.