Deprecated: Methods with the same name as their class will not be constructors in a future version of PHP; plgContentJComments has a deprecated constructor in /var/www/astarmathsandphysics/plugins/content/jcomments/jcomments.php on line 25 Call Stack: 0.0001 362584 1. {main}() /var/www/astarmathsandphysics/index.php:0 0.1138 1213480 2. Joomla\CMS\Application\SiteApplication->execute() /var/www/astarmathsandphysics/index.php:49 0.1138 1213480 3. Joomla\CMS\Application\SiteApplication->doExecute() /var/www/astarmathsandphysics/libraries/src/Application/CMSApplication.php:267 0.2154 4200232 4. Joomla\CMS\Application\SiteApplication->dispatch() /var/www/astarmathsandphysics/libraries/src/Application/SiteApplication.php:233 0.2169 4227992 5. Joomla\CMS\Component\ComponentHelper::renderComponent() /var/www/astarmathsandphysics/libraries/src/Application/SiteApplication.php:194 0.2176 4245704 6. Joomla\CMS\Component\ComponentHelper::executeComponent() /var/www/astarmathsandphysics/libraries/src/Component/ComponentHelper.php:356 0.2178 4276224 7. require_once('/var/www/astarmathsandphysics/components/com_content/content.php') /var/www/astarmathsandphysics/libraries/src/Component/ComponentHelper.php:381 0.2188 4298944 8. ContentController->execute() /var/www/astarmathsandphysics/components/com_content/content.php:42 0.2188 4298944 9. ContentController->display() /var/www/astarmathsandphysics/libraries/src/MVC/Controller/BaseController.php:710 0.2811 4967792 10. ContentController->display() /var/www/astarmathsandphysics/components/com_content/controller.php:113 0.2850 5159944 11. Joomla\CMS\Cache\Controller\ViewController->get() /var/www/astarmathsandphysics/libraries/src/MVC/Controller/BaseController.php:663 0.2856 5180872 12. ContentViewArticle->display() /var/www/astarmathsandphysics/libraries/src/Cache/Controller/ViewController.php:102 0.2979 5390176 13. Joomla\CMS\Plugin\PluginHelper::importPlugin() /var/www/astarmathsandphysics/components/com_content/views/article/view.html.php:189 0.2979 5390432 14. Joomla\CMS\Plugin\PluginHelper::import() /var/www/astarmathsandphysics/libraries/src/Plugin/PluginHelper.php:182

The Importance of Simple Harmonic Motion

Any vibration where the force exerted on a body is proportion to the displacement from equilibrium is simple harmonic.
This includes all systems obeying Hook'e's Law,  \(\mathbf{F}=-k \mathbf{x}\).
By letting  \(\mathbf{F} = m \mathbf{a}\)  we get  \(m \mathbf{a} - k \mathbf{x} \rightarrow a = - \frac{k}{m} \mathbf{x} = - \omega^2 x\).
Actually, a system does not need to obey Hooke's Law to any great extent to execute simple harmonic motion. If the vibrations are small enough, most vibrations are approximately simple harmonic. Often this can produce important results. By assuming that the Vibrations of atoms in a crystal lattice are simple harmonic we obtain the important equation  \(E=mc \theta\)