{"id":455,"date":"2023-06-17T06:32:05","date_gmt":"2023-06-17T06:32:05","guid":{"rendered":"https:\/\/physigeek.com\/id\/pendulum-sederhana\/"},"modified":"2023-06-17T06:32:05","modified_gmt":"2023-06-17T06:32:05","slug":"pendulum-sederhana","status":"publish","type":"post","link":"https:\/\/physigeek.com\/id\/pendulum-sederhana\/","title":{"rendered":"Pendulum sederhana"},"content":{"rendered":"<p>Artikel ini menjelaskan apa itu pendulum sederhana dan apa saja ciri-cirinya. Disajikan juga rumus-rumus yang menjelaskan tentang gerak bandul sederhana, dan selain itu Anda juga dapat melihat apa saja hukum-hukum bandul sederhana. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%C2%BFQue-es-un-pendulo-simple\"><\/span> Apa itu pendulum sederhana?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Bandul sederhana<\/strong> , disebut juga <strong>bandul matematika<\/strong> atau <strong>bandul ideal<\/strong> , adalah suatu sistem yang terdiri atas partikel bermassa yang digantungkan pada suatu titik tetap melalui kawat dengan panjang tertentu.<\/p>\n<p> Dalam fisika, pendulum sederhana digunakan untuk mempelajari gerak osilasi suatu massa yang tersuspensi. Jika suatu gaya diterapkan pada suatu massa, maka massa tersebut akan berosilasi melampaui posisi kesetimbangannya dan oleh karena itu menggambarkan suatu gerak osilasi.<\/p>\n<p> Lebih tepatnya, gerak yang dilakukan oleh massa bandul sederhana disebut <strong>gerak bandul<\/strong> , yaitu <a href=\"https:\/\/physigeek.com\/id\/gerakan-periodik\/\">gerak periodik<\/a> karena massa melewati posisi yang sama setiap selang waktu tertentu. <\/p>\n<div style=\"background-color:#FFFDE7; padding-top: 10px; padding-bottom: 10px; padding-right: 10px; padding-left: 20px; border: 2.5px dashed #FFB74D; border-radius:20px;\"> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>Lihat:<\/strong> <a href=\"https:\/\/physigeek.com\/id\/gerakan-pendulum\/\">Apa itu gerak pendulum?<\/a> <\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Caracteristicas-de-un-pendulo-simple\"><\/span> Ciri-ciri bandul sederhana<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Bandul sederhana ditentukan oleh ciri-ciri atau bagian-bagiannya sebagai berikut:<\/p>\n<ul style=\"color:#4fd12f; font-weight: bold;\">\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>Panjang (\u2113)<\/strong> : adalah panjang tali yang bergerak dari titik tetap bandul sederhana ke titik berat benda yang melakukan gerak bandul.<\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>Osilasi<\/strong> : adalah busur yang dilalui massa antara posisi ekstrim bandul sederhana ditambah kembalinya ke posisi semula.<\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>Periode (T)<\/strong> : adalah waktu yang diperlukan untuk menyelesaikan suatu getaran.<\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>Frekuensi (f)<\/strong> : adalah banyaknya osilasi yang dilakukan bandul sederhana tiap satuan waktu.<\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>Sudut (\u03b8)<\/strong> : adalah sudut yang dibentuk oleh tali pendulum dan garis vertikal.<\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>Amplitudo (\u0398)<\/strong> : adalah sudut yang dibentuk oleh garis vertikal dan tali busur bandul sederhana ketika berada pada posisi ekstrim.<\/span> <\/li>\n<\/ul>\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/uploads\/2023\/09\/mouvement-pendulaire.png\" alt=\"ciri-ciri bandul sederhana, bagian-bagian bandul sederhana, unsur-unsur bandul sederhana\" class=\"wp-image-8900\" width=\"430\" height=\"346\" srcset=\"https:\/\/physigeek.com\/wp-content\/uploads\/2023\/09\/mouvement-pendulaire-300x242.png 300w, https:\/\/physigeek.com\/wp-content\/uploads\/2023\/09\/mouvement-pendulaire-768x619.png 768w, https:\/\/physigeek.com\/wp-content\/uploads\/2023\/09\/mouvement-pendulaire.png 910w\" sizes=\"(max-width: 300px) 100vw, 300px\"><\/figure>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Formulas-del-pendulo-simple\"><\/span> Rumus pendulum sederhana <span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Ecuacion-diferencial-del-pendulo-simple\"><\/span> Persamaan diferensial sederhana pendulum<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> Persamaan diferensial pendulum sederhana menyatakan bahwa jumlah panjang tali dikali percepatan sudut ditambah percepatan gravitasi dikali sinus sudut yang dibentuk tali terhadap vertikal adalah sama dengan nol.<\/p>\n<p> Jadi, <strong>persamaan diferensial bandul sederhana<\/strong> adalah:<\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-538fb79a964706dd993084143e043434_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\ell\\cdot \\ddot{\\theta}+g\\cdot \\text{sen}(\\theta)=0\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"153\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\"margin-bottom:5px\"> Emas: <\/p>\n<ul style=\"color:#4fd12f; font-weight: bold;\">\n<li style=\"margin-bottom:5px\"><span style=\"color:#101010;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-a01f1555785d2234d4294020a2e3968a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\ell\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p> adalah panjang pendulum. <\/span><\/li>\n<li style=\"margin-bottom:5px\"><span style=\"color:#101010;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-273485de50bb5d8bc82bf426ab9a4bec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\ddot{\\theta}\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> adalah percepatan sudut. <\/span><\/li>\n<li style=\"margin-bottom:5px\"><span style=\"color:#101010;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-7b2034939b850e3311120fca462ab64e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\theta\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> adalah sudut yang dibentuk tali pendulum terhadap vertikal. <\/span><\/li>\n<li style=\"margin-bottom:5px\"><span style=\"color:#101010;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-e88010d25c51c0c42c505ee1004ed182_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"g\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\"><\/p>\n<p> adalah percepatan gravitasi yang nilainya di Bumi adalah 9,81 m\/s <sup>2<\/sup> .<\/span><\/li>\n<\/ul>\n<p> Jika pendulum sederhana menimbulkan osilasi dengan amplitudo kecil, maka perkiraan sin(\u03b8)\u2248\u03b8 dapat dibuat. Dalam hal ini persamaan diferensial bandul sederhana adalah sebagai berikut: <\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-ac8702a652711a416d848626edc80540_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\ell\\cdot \\ddot{\\theta}+g\\cdot \\theta=0\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"114\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Ecuacion-del-movimiento-del-pendulo-simple\"><\/span> Persamaan gerak bandul sederhana<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> Menyelesaikan persamaan diferensial yang terlihat pada bagian di atas, kita sampai pada persamaan yang menggambarkan sudut pergerakan bandul sederhana relatif terhadap posisi kesetimbangannya:<\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-ee038d945fb195a2a70d1effc316d069_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\theta=\\Theta\\cdot\\text{sin}(\\omega\\cdot t+\\phi)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"157\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\"margin-bottom:5px\"> Emas: <\/p>\n<ul style=\"color:#4fd12f; font-weight: bold;\">\n<li style=\"margin-bottom:5px\"><span style=\"color:#101010;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-7b2034939b850e3311120fca462ab64e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\theta\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> adalah sudut yang dibentuk oleh tali pendulum sederhana dan tali. <\/span><\/li>\n<li style=\"margin-bottom:5px\"><span style=\"color:#101010;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-309d1e9dc1d3a46c23ed1f6d2449b454_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\Theta\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"13\" style=\"vertical-align: 0px;\"><\/p>\n<p> adalah amplitudo pendulum sederhana. <\/span><\/li>\n<li style=\"margin-bottom:5px\"><span style=\"color:#101010;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-fbffdce91996e0a17795d82e8e6996d9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\omega\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\"><\/p>\n<p> adalah pulsasi atau frekuensi sudut pendulum sederhana. <\/span><\/li>\n<li style=\"margin-bottom:5px\"><span style=\"color:#101010;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-fd9cb27edab3f0a8a249bc80cc9c6ee2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"t\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"6\" style=\"vertical-align: 0px;\"><\/p>\n<p> adalah saat di mana sudut dihitung. <\/span><\/li>\n<li style=\"margin-bottom:5px\"><span style=\"color:#101010;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-8358131e7f71b02f5a1b767b67603090_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\phi\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"11\" style=\"vertical-align: -4px;\"><\/p>\n<p> adalah fase awal pendulum sederhana.<\/span><\/li>\n<\/ul>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Periodo-del-pendulo-simple\"><\/span> Periode pendulum sederhana<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> Untuk osilasi kecil, periode osilasi bandul sederhana sama dengan dua kali pi dikalikan akar kuadrat perbandingan panjang tali bandul dengan percepatan gravitasi.<\/p>\n<p> Oleh karena itu, <strong>rumus menghitung periode osilasi bandul sederhana<\/strong> dengan amplitudo osilasi kecil adalah sebagai berikut:<\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-49774e684263aae5d8703f86c9ed09b9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle T=2\\pi\\sqrt{\\frac{\\ell}{g}}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"87\" style=\"vertical-align: -21px;\"><\/p>\n<\/p>\n<p style=\"margin-bottom:5px\"> Emas: <\/p>\n<ul style=\"color:#4fd12f; font-weight: bold;\">\n<li style=\"margin-bottom:5px\"><span style=\"color:#101010;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-7e093fd43ad2c244140c11afe4d4bdff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"T\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"13\" style=\"vertical-align: 0px;\"><\/p>\n<p> adalah periode bandul sederhana. <\/span><\/li>\n<li style=\"margin-bottom:5px\"><span style=\"color:#101010;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-a01f1555785d2234d4294020a2e3968a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\ell\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p> adalah panjang tali bandul sederhana. <\/span><\/li>\n<li style=\"margin-bottom:5px\"><span style=\"color:#101010;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-e88010d25c51c0c42c505ee1004ed182_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"g\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\"><\/p>\n<p> adalah percepatan gravitasi yang nilainya di Bumi adalah 9,81 m\/s <sup>2<\/sup> . <\/span><\/li>\n<\/ul>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Leyes-del-pendulo-simple\"><\/span>Hukum pendulum sederhana<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Dalam fisika, ada empat hukum yang menentukan gerak osilasi bandul sederhana:<\/p>\n<ul style=\"color:#4fd12f; font-weight: bold;\">\n<li style=\"margin-bottom:20px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>Hukum kebebasan massa<\/strong> : Dua buah bandul yang talinya sama panjang mempunyai periode yang sama berapapun massa yang digantungkan pada tali tersebut. Dengan kata lain, dua bandul yang massanya berbeda akan mempunyai periode yang sama jika panjang talinya sama.<\/span><\/li>\n<li style=\"margin-bottom:20px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>Hukum isokronisme<\/strong> : periode bandul sederhana tidak bergantung pada amplitudo gerak. Jadi, jika dua bandul sederhana mempunyai panjang tali yang sama, periodenya akan tetap ekuivalen meskipun amplitudonya berbeda.<\/span><\/li>\n<li style=\"margin-bottom:20px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>Hukum panjang<\/strong> : periode osilasi suatu gerak bandul sebanding dengan panjang tali bandul. Jadi, semakin panjang talinya, semakin besar periode bandulnya.<\/span><\/li>\n<li style=\"margin-bottom:20px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>Hukum Percepatan Gravitasi<\/strong> : Percepatan gravitasi mempengaruhi periode osilasi gerak bandul, sehingga periode bandul akan berubah tergantung pada gaya gravitasi tempat tersebut. Semakin besar gaya gravitasi maka semakin pendek periode osilasi pendulum.<\/span><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Artikel ini menjelaskan apa itu pendulum sederhana dan apa saja ciri-cirinya. Disajikan juga rumus-rumus yang menjelaskan tentang gerak bandul sederhana, dan selain itu Anda juga dapat melihat apa saja hukum-hukum bandul sederhana. Apa itu pendulum sederhana? Bandul sederhana , disebut juga bandul matematika atau bandul ideal , adalah suatu sistem yang terdiri atas partikel bermassa &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/physigeek.com\/id\/pendulum-sederhana\/\"> <span class=\"screen-reader-text\">Pendulum sederhana<\/span> Baca selengkapnya &quot;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"","footnotes":""},"categories":[3],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.4 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u25b7 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