# Oscillations¶

### Angular frequency ($\omega$) and period ( $T$)¶

$$ \large \omega = \frac{2 \pi}{T} $$## Simple Pendulum¶

### Angular Frequency¶

$$ \large \omega = \sqrt{\frac{g}{L}} $$where

$L$: length of the pendulum

$g$: acceleration of gravity

### Period¶

$$ \large T = 2\pi \sqrt{\frac{L}{g}} $$Note that the period of a pendulum is independent of mass.

### Related Problems¶

- GRE Physics GR1777 Problem 003
- GRE Physics GR0877 Problem 059

## Spring¶

### Angluar Frequency¶

$$ \large \omega = \sqrt{\frac{k}{m}} $$### Period¶

$$ \large T = 2\pi \sqrt{\frac{m}{k}} $$### Potential Energy¶

$$ \large E = \frac{1}{2} k x^2 $$### Spring Constant¶

#### Serial Connection¶

$$ \frac{1}{k_\text{eff}} = \frac{1}{k_1} + \frac{1}{k_2} $$#### Parallel Connection¶

$$ k_\text{eff} = k_1 + k_2 $$### Related Problems¶

- GRE Physics GR0177 Problem 090