Oscillations

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.

  • 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

$$ k_\text{eff} = k_1 + k_2 $$
  • GRE Physics GR0177 Problem 090

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