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PHYS 122 Notes

Table of Contents

1 Simple Harmonic Motion

Useful Formula
$\omega=\frac{\Delta\theta}{\Delta t}=\frac{2\pi}{T}=2\pi f$
$x=x_0\cos(\omega t)$ describes the object that is at $x=x_0$ at $t=0$.
General Equation: $x=x_0\cos(\omega t + \phi)$
$$\begin{align*} \frac{dx}{dt}&=\frac{d}{dt} x_0\cos(\omega t + \phi)\\ v&= -\omega x_0\sin(\omega t + \phi)\\ a&= -\omega^2 x_0\cos(\omega t + \phi)=-\omega^2 x \end{align*}$$
A simple harmonic oscillator is:
  • A projection of an object moving in a circle.
  • An object whose acceleration is proportional to its position.
e.g. For an object on a spring undergoing simple harmonic motion, $$\begin{align*} F&=-kx\\ ma&= -kx\\ a&= -\frac{k}{m}x\\ \therefore \frac{k}{m}&=\omega^2\\ \omega &= \sqrt{\frac{k}{m}} \end{align*}$$

2 Electricity

Electric Potentials

$$\Delta V=\frac{\Delta U}{q}=-\int_a^b\vec{E}\cdot d\vec{r}$$ $$V_{ab}=V_a-V_b=-\int_b^a\vec{E}\cdot d\vec{r}=\int_a^b\vec{E}\cdot d\vec{r}$$
To find the electric field given Electric Potential at a certain radial distance, $$E_r=-\frac{\delta V}{\delta r}$$

Calculating Capacitance of Spheres/Cylinders

  1. Find Potential Difference between outer and inner shell. Treat cylinders as lines of charge and spheres as a point charge.
  2. Use $C=\frac{Q}{\Delta V}$ ($Q$ should cancel out)

Capacitance of Circuits

3 Magnetism

Magnetic Forces in a Magnetic Field

Magnetic Field Sources

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