<p align="right">Last Update: <font color="#4f81bd">November 26, 2024</font></p> ## BIG IDEAS - Period ($T$) is the time for one cycle of oscillation. - The [[SI units|SI unit]] is seconds (*s*). - Inverse relationship to [[Frequency|frequency]]. --- ### Period of Mass-Spring - Mass $m$ and the force constant $k$ affect the period and frequency of [[Simple Harmonic Motion|simple harmonic motion]]. - A period is the time taken by an object to complete one cycle of oscillation (back and forth). It is measured in seconds. ### Formulas $T=2 \pi \sqrt \frac{m}{k} \tag{1}$ Where $T$ is the period, $m$ is the mass, and $k$ is the spring constant. - The inverse of period is frequency ( ) and has a unit of Hertz (abbreviated Hz). A hertz is $\frac{1}{s}$ $T = \frac{1}{f}$ - Frequency and period are different ways of expressing the same concept. $f = \frac{1}{2 \pi}\sqrt \frac{k}{m}$ ### Period of a Pendulum The period of oscillation ($T$ ) is dependent on the length of the pendulum ($L$ ) and NOT the mass (the bob). Therefore, the period is calculated by knowing the $L$ of the pendulum and the gravitational field strength ($g$ ). $T=2\pi\sqrt\frac{L}{g}$ Where $T$ is the period, $L$ is length and $g$ is the acceleration due to gravity (gravitational field strength). It’s possible to solve for $g$, thus a pendulum is a means to calculate $g$. ### Example problem A mass oscillates 20 times. A stopwatch is used to measure time. Take the time on the stopwatch and divide it by 20 (number of oscillations) to get the period. To get frequency, take the inverse of the period. ### Slide Deck <div style="position: relative; width: 100%; height: 0; padding-top: 56.2500%; padding-bottom: 0; box-shadow: 0 2px 8px 0 rgba(63,69,81,0.16); margin-top: 1.6em; margin-bottom: 0.9em; overflow: hidden; border-radius: 8px; will-change: transform;"> <iframe loading="lazy" style="position: absolute; width: 100%; height: 100%; top: 0; left: 0; border: none; padding: 0;margin: 0;" src="https://www.canva.com/design/DAGSvfWZmgc/msVvc-BIidCkZpEPVOgmqQ/view?embed" allowfullscreen="allowfullscreen" allow="fullscreen"> </iframe> </div> ### Related Topics --- [[Home|Home]] | [[Oscillations]] | [[Periodic Motion]] | [[Simple Harmonic Motion]] | [[Amplitude]] | [[Period]] | [[Frequency]] | [[Waves]] | [[Module 0 Sound]] | [[Electromagnetic radiation]] | [[Waves]] | [[Module 0 Sound]] | [[Electromagnetic radiation]]