{"id":88284,"date":"2025-06-01T07:07:05","date_gmt":"2025-06-01T07:07:05","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=88284"},"modified":"2025-06-01T07:07:05","modified_gmt":"2025-06-01T07:07:05","slug":"a-particle-is-executing-simple-harmonic-motion-which-one-of-the-follo","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/a-particle-is-executing-simple-harmonic-motion-which-one-of-the-follo\/","title":{"rendered":"A particle is executing simple harmonic motion. Which one of the follo"},"content":{"rendered":"

A particle is executing simple harmonic motion. Which one of the following statements about the acceleration of the oscillating particle is true ?<\/p>\n

[amp_mcq option1=”It is always in the opposite direction to velocity” option2=”It is proportional to the frequency of oscillation” option3=”It is minimum when the speed is maximum” option4=”It decreases as the potential energy increases” correct=”option3″]<\/p>\n

\n
\n
This question was previously asked in<\/div>\n
UPSC NDA-2 – 2016<\/div>\n<\/div>\n
Download PDF<\/a>Attempt Online<\/a><\/div>\n<\/div>\n
\nIn simple harmonic motion, the acceleration of the oscillating particle is minimum when the speed is maximum.
\n<\/section>\n
\nSimple Harmonic Motion (SHM) is characterized by an acceleration that is directly proportional to the displacement from the equilibrium position and is always directed towards the equilibrium position (a = -\u03c9\u00b2x, where x is displacement and \u03c9 is angular frequency). The equilibrium position is where the displacement x = 0. At this point, the restoring force and acceleration are zero, representing the minimum magnitude of acceleration. In SHM, the speed of the particle is maximum at the equilibrium position (x=0) and zero at the extreme positions (maximum |x|). Thus, acceleration (minimum at x=0) is minimum when speed (maximum at x=0) is maximum.
\n<\/section>\n
\nOption A is incorrect; acceleration is in the opposite direction to velocity only when the object is slowing down (moving away from equilibrium). When moving towards equilibrium, velocity and acceleration are in the same direction. Option B is incorrect; acceleration is proportional to the *square* of the angular frequency (\u03c9\u00b2), not frequency directly, though frequency is proportional to \u03c9. Option D is incorrect; potential energy is maximum at the extreme positions where |x| is maximum, and acceleration magnitude |a| = \u03c9\u00b2|x| is also maximum there. So, as potential energy increases, acceleration magnitude increases, not decreases.
\n<\/section>\n","protected":false},"excerpt":{"rendered":"

A particle is executing simple harmonic motion. Which one of the following statements about the acceleration of the oscillating particle is true ? [amp_mcq option1=”It is always in the opposite direction to velocity” option2=”It is proportional to the frequency of oscillation” option3=”It is minimum when the speed is maximum” option4=”It decreases as the potential energy … <\/p>\n

Detailed SolutionA particle is executing simple harmonic motion. Which one of the follo<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1094],"tags":[1098,1129,1128],"class_list":["post-88284","post","type-post","status-publish","format-standard","hentry","category-upsc-nda-2","tag-1098","tag-mechanics","tag-physics","no-featured-image-padding"],"yoast_head":"\nA particle is executing simple harmonic motion. Which one of the follo<\/title>\n<meta name=\"description\" content=\"In simple harmonic motion, the acceleration of the oscillating particle is minimum when the speed is maximum. Simple Harmonic Motion (SHM) is characterized by an acceleration that is directly proportional to the displacement from the equilibrium position and is always directed towards the equilibrium position (a = -\u03c9\u00b2x, where x is displacement and \u03c9 is angular frequency). The equilibrium position is where the displacement x = 0. At this point, the restoring force and acceleration are zero, representing the minimum magnitude of acceleration. In SHM, the speed of the particle is maximum at the equilibrium position (x=0) and zero at the extreme positions (maximum |x|). Thus, acceleration (minimum at x=0) is minimum when speed (maximum at x=0) is maximum.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/exam.pscnotes.com\/mcq\/a-particle-is-executing-simple-harmonic-motion-which-one-of-the-follo\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"A particle is executing simple harmonic motion. Which one of the follo\" \/>\n<meta property=\"og:description\" content=\"In simple harmonic motion, the acceleration of the oscillating particle is minimum when the speed is maximum. Simple Harmonic Motion (SHM) is characterized by an acceleration that is directly proportional to the displacement from the equilibrium position and is always directed towards the equilibrium position (a = -\u03c9\u00b2x, where x is displacement and \u03c9 is angular frequency). The equilibrium position is where the displacement x = 0. At this point, the restoring force and acceleration are zero, representing the minimum magnitude of acceleration. In SHM, the speed of the particle is maximum at the equilibrium position (x=0) and zero at the extreme positions (maximum |x|). Thus, acceleration (minimum at x=0) is minimum when speed (maximum at x=0) is maximum.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/a-particle-is-executing-simple-harmonic-motion-which-one-of-the-follo\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T07:07:05+00:00\" \/>\n<meta name=\"author\" content=\"rawan239\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"rawan239\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" \/>\n<!-- \/ Yoast SEO Premium plugin. -->","yoast_head_json":{"title":"A particle is executing simple harmonic motion. Which one of the follo","description":"In simple harmonic motion, the acceleration of the oscillating particle is minimum when the speed is maximum. Simple Harmonic Motion (SHM) is characterized by an acceleration that is directly proportional to the displacement from the equilibrium position and is always directed towards the equilibrium position (a = -\u03c9\u00b2x, where x is displacement and \u03c9 is angular frequency). The equilibrium position is where the displacement x = 0. At this point, the restoring force and acceleration are zero, representing the minimum magnitude of acceleration. In SHM, the speed of the particle is maximum at the equilibrium position (x=0) and zero at the extreme positions (maximum |x|). Thus, acceleration (minimum at x=0) is minimum when speed (maximum at x=0) is maximum.","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/exam.pscnotes.com\/mcq\/a-particle-is-executing-simple-harmonic-motion-which-one-of-the-follo\/","og_locale":"en_US","og_type":"article","og_title":"A particle is executing simple harmonic motion. Which one of the follo","og_description":"In simple harmonic motion, the acceleration of the oscillating particle is minimum when the speed is maximum. Simple Harmonic Motion (SHM) is characterized by an acceleration that is directly proportional to the displacement from the equilibrium position and is always directed towards the equilibrium position (a = -\u03c9\u00b2x, where x is displacement and \u03c9 is angular frequency). The equilibrium position is where the displacement x = 0. At this point, the restoring force and acceleration are zero, representing the minimum magnitude of acceleration. In SHM, the speed of the particle is maximum at the equilibrium position (x=0) and zero at the extreme positions (maximum |x|). Thus, acceleration (minimum at x=0) is minimum when speed (maximum at x=0) is maximum.","og_url":"https:\/\/exam.pscnotes.com\/mcq\/a-particle-is-executing-simple-harmonic-motion-which-one-of-the-follo\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2025-06-01T07:07:05+00:00","author":"rawan239","twitter_card":"summary_large_image","twitter_misc":{"Written by":"rawan239","Est. reading time":"1 minute"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/exam.pscnotes.com\/mcq\/a-particle-is-executing-simple-harmonic-motion-which-one-of-the-follo\/","url":"https:\/\/exam.pscnotes.com\/mcq\/a-particle-is-executing-simple-harmonic-motion-which-one-of-the-follo\/","name":"A particle is executing simple harmonic motion. 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Thus, acceleration (minimum at x=0) is minimum when speed (maximum at x=0) is maximum.","breadcrumb":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/a-particle-is-executing-simple-harmonic-motion-which-one-of-the-follo\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/exam.pscnotes.com\/mcq\/a-particle-is-executing-simple-harmonic-motion-which-one-of-the-follo\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/exam.pscnotes.com\/mcq\/a-particle-is-executing-simple-harmonic-motion-which-one-of-the-follo\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/exam.pscnotes.com\/mcq\/"},{"@type":"ListItem","position":2,"name":"UPSC NDA-2","item":"https:\/\/exam.pscnotes.com\/mcq\/category\/upsc-nda-2\/"},{"@type":"ListItem","position":3,"name":"A particle is executing simple harmonic motion. 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