{"id":161232,"date":"2023-10-25T13:37:16","date_gmt":"2023-10-25T08:07:16","guid":{"rendered":"https:\/\/www.gkseries.com\/blog\/?p=161232"},"modified":"2023-10-25T13:37:18","modified_gmt":"2023-10-25T08:07:18","slug":"the-equation-of-motion-for-a-spring-mass-system-excited-by-a-harmonic-force-is","status":"publish","type":"post","link":"https:\/\/www.gkseries.com\/blog\/the-equation-of-motion-for-a-spring-mass-system-excited-by-a-harmonic-force-is\/","title":{"rendered":"The equation of motion for a spring-mass system excited by a harmonic force is"},"content":{"rendered":"\n<p>Q. The equation of motion for a spring-mass system excited by a harmonic force is<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"278\" height=\"48\" src=\"https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2023\/10\/Screenshot-1042.png\" alt=\"\" class=\"wp-image-161233\"\/><\/figure>\n\n\n\n<p><span style=\"font-size:11.0pt;font-family:&quot;Times New Roman&quot;,serif;\nmso-fareast-font-family:&quot;Times New Roman&quot;;mso-ansi-language:EN-US;mso-fareast-language:\nEN-US;mso-bidi-language:AR-SA\">where<span style=\"letter-spacing:-.55pt\"> <\/span><\/span><i><span style=\"font-size:11.5pt;mso-bidi-font-size:\n11.0pt;font-family:&quot;Times New Roman&quot;,serif;mso-fareast-font-family:&quot;Times New Roman&quot;;\nmso-ansi-language:EN-US;mso-fareast-language:EN-US;mso-bidi-language:AR-SA\">M<span style=\"letter-spacing:1.15pt\"> <\/span><\/span><\/i><span style=\"font-size:11.0pt;\nfont-family:&quot;Times New Roman&quot;,serif;mso-fareast-font-family:&quot;Times New Roman&quot;;\nmso-ansi-language:EN-US;mso-fareast-language:EN-US;mso-bidi-language:AR-SA\">is<span style=\"letter-spacing:-.25pt\"> <\/span>the<span style=\"letter-spacing:-.3pt\"> <\/span>mass,<span style=\"letter-spacing:2.1pt\"> <\/span><\/span><i><span style=\"font-size:11.5pt;mso-bidi-font-size:11.0pt;font-family:&quot;Times New Roman&quot;,serif;\nmso-fareast-font-family:&quot;Times New Roman&quot;;mso-ansi-language:EN-US;mso-fareast-language:\nEN-US;mso-bidi-language:AR-SA\">K<span style=\"letter-spacing:2.55pt\"> <\/span><\/span><\/i><span style=\"font-size:11.0pt;font-family:&quot;Times New Roman&quot;,serif;mso-fareast-font-family:\n&quot;Times New Roman&quot;;mso-ansi-language:EN-US;mso-fareast-language:EN-US;\nmso-bidi-language:AR-SA\">is<span style=\"letter-spacing:-.25pt\"> <\/span>the<span style=\"letter-spacing:-.3pt\"> <\/span>spring<span style=\"letter-spacing:-.4pt\"> <\/span>stiffness,<span style=\"letter-spacing:2.15pt\"> <\/span><\/span><i><span style=\"font-size:11.5pt;mso-bidi-font-size:11.0pt;font-family:\n&quot;Times New Roman&quot;,serif;mso-fareast-font-family:&quot;Times New Roman&quot;;mso-ansi-language:\nEN-US;mso-fareast-language:EN-US;mso-bidi-language:AR-SA\">F<span style=\"letter-spacing:.6pt\"> <\/span><\/span><\/i><span style=\"font-size:11.0pt;\nfont-family:&quot;Times New Roman&quot;,serif;mso-fareast-font-family:&quot;Times New Roman&quot;;\nmso-ansi-language:EN-US;mso-fareast-language:EN-US;mso-bidi-language:AR-SA\">is<span style=\"letter-spacing:-.25pt\"> <\/span>the<span style=\"letter-spacing:-.3pt\"> <\/span>force<span style=\"letter-spacing:-.4pt\"> <\/span>amplitude<span style=\"letter-spacing:-.35pt\"> <\/span>and<span style=\"letter-spacing:.15pt\"> <\/span><\/span><span style=\"font-size:12.5pt;mso-bidi-font-size:11.0pt;font-family:Symbol;\nmso-fareast-font-family:&quot;Times New Roman&quot;;mso-bidi-font-family:&quot;Times New Roman&quot;;\nmso-ansi-language:EN-US;mso-fareast-language:EN-US;mso-bidi-language:AR-SA\">w<\/span><span style=\"font-size:12.5pt;mso-bidi-font-size:11.0pt;font-family:&quot;Times New Roman&quot;,serif;\nmso-fareast-font-family:&quot;Times New Roman&quot;;letter-spacing:-.7pt;mso-ansi-language:\nEN-US;mso-fareast-language:EN-US;mso-bidi-language:AR-SA\"> <\/span><span style=\"font-size:11.0pt;font-family:&quot;Times New Roman&quot;,serif;mso-fareast-font-family:\n&quot;Times New Roman&quot;;mso-ansi-language:EN-US;mso-fareast-language:EN-US;\nmso-bidi-language:AR-SA\">is<span style=\"letter-spacing:-.25pt\"> <\/span>the<span style=\"letter-spacing:-.2pt\"> <\/span>angular<span style=\"letter-spacing:-2.85pt\"> <\/span>frequency<span style=\"letter-spacing:-.3pt\"> <\/span>of excitation. Resonance<span style=\"letter-spacing:-.05pt\"> <\/span>occurs<span style=\"letter-spacing:-.05pt\"> <\/span>when<span style=\"letter-spacing:.25pt\"> <\/span><\/span><span style=\"font-size:12.5pt;mso-bidi-font-size:11.0pt;font-family:Symbol;\nmso-fareast-font-family:&quot;Times New Roman&quot;;mso-bidi-font-family:&quot;Times New Roman&quot;;\nmso-ansi-language:EN-US;mso-fareast-language:EN-US;mso-bidi-language:AR-SA\">w<\/span><span style=\"font-size:12.5pt;mso-bidi-font-size:11.0pt;font-family:&quot;Times New Roman&quot;,serif;\nmso-fareast-font-family:&quot;Times New Roman&quot;;letter-spacing:-.35pt;mso-ansi-language:\nEN-US;mso-fareast-language:EN-US;mso-bidi-language:AR-SA\"> <\/span><span style=\"font-size:11.0pt;font-family:&quot;Times New Roman&quot;,serif;mso-fareast-font-family:\n&quot;Times New Roman&quot;;mso-ansi-language:EN-US;mso-fareast-language:EN-US;\nmso-bidi-language:AR-SA\">is<span style=\"letter-spacing:.1pt\"> <\/span>equal<span style=\"letter-spacing:-.05pt\"> <\/span>to<\/span><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"703\" height=\"79\" src=\"https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2023\/10\/Screenshot-1043.png\" alt=\"\" class=\"wp-image-161234\" srcset=\"https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2023\/10\/Screenshot-1043.png 703w, https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2023\/10\/Screenshot-1043-300x34.png 300w\" sizes=\"(max-width: 703px) 100vw, 703px\" \/><\/figure>\n\n\n\n<p>Ans: Option D<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Q. The equation of motion for a spring-mass system excited by a harmonic force is where M is the mass, K is the spring stiffness, F is the force amplitude and w is the angular frequency of excitation. Resonance occurs when w is equal to Ans: Option D<\/p>\n","protected":false},"author":419,"featured_media":161235,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","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":"","ast-disable-related-posts":"","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":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[5141],"tags":[5140],"class_list":["post-161232","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-gate","tag-gate-questions"],"_links":{"self":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/161232","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/users\/419"}],"replies":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/comments?post=161232"}],"version-history":[{"count":1,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/161232\/revisions"}],"predecessor-version":[{"id":161236,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/161232\/revisions\/161236"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media\/161235"}],"wp:attachment":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media?parent=161232"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/categories?post=161232"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/tags?post=161232"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}