{"id":850,"date":"2025-10-16T15:46:07","date_gmt":"2025-10-16T15:46:07","guid":{"rendered":"https:\/\/ibphysicswithrao.com\/home\/?p=850"},"modified":"2025-10-17T02:47:45","modified_gmt":"2025-10-17T02:47:45","slug":"the-secret-language-of-oscillations-why-your-favorite-physics-equations-fail-for-shm","status":"publish","type":"post","link":"https:\/\/ibphysicswithrao.com\/home\/the-secret-language-of-oscillations-why-your-favorite-physics-equations-fail-for-shm\/","title":{"rendered":"The Secret Language of Oscillations: Why Your Favorite Physics Equations Fail for SHM"},"content":{"rendered":"\n<h3 class=\"wp-block-heading\">When Your Go-To Equations Give Up<\/h3>\n\n\n\n<p>Think about the world around you: a pendulum swinging in a clock, a guitar string vibrating to make a note, or even a bungee jumper bouncing up and down. These are all examples of a special kind of rhythmic motion called <strong>Simple Harmonic Motion (SHM)<\/strong>.<\/p>\n\n\n\n<p>In your physics class, you&#8217;ve probably become good friends with the kinematics equations:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img fetchpriority=\"high\" decoding=\"async\" width=\"414\" height=\"347\" src=\"https:\/\/ibphysicswithrao.com\/home\/wp-content\/uploads\/2025\/10\/image-5.png\" alt=\"\" class=\"wp-image-851\" srcset=\"https:\/\/ibphysicswithrao.com\/home\/wp-content\/uploads\/2025\/10\/image-5.png 414w, https:\/\/ibphysicswithrao.com\/home\/wp-content\/uploads\/2025\/10\/image-5-300x251.png 300w\" sizes=\"(max-width: 414px) 100vw, 414px\" \/><\/figure><\/div>\n\n\n<p>These equations are fantastic for figuring out the motion of a ball thrown in the air or a car accelerating down a road. But here\u2019s the puzzle: the moment you try to use them on a swinging pendulum or a bouncing spring, they completely fail. Why do these powerful tools fall silent when faced with the simple, repeating dance of SHM? Let&#8217;s find out.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">The Core Problem: A Constantly Changing Acceleration<\/h3>\n\n\n\n<p>The kinematics equations you know and love have one critical weakness: <strong>they only work when acceleration is constant.<\/strong> For SHM, acceleration is the exact opposite\u2014it&#8217;s <em>always<\/em> changing!<\/p>\n\n\n\n<p>This leads to one of the most common misconceptions. Consider a typical exam question from one of our videos:<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe title=\"13. A mass is oscillating with simple harmonic motion. At time t, the acceleration is at a positive\" width=\"640\" height=\"360\" src=\"https:\/\/www.youtube.com\/embed\/fzKzJ9BuCPg?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n<\/div><\/figure>\n<\/blockquote>\n\n\n\n<p>The acceleration of the object is always proportional to its displacement, and it points in the opposite direction. Think of a spring: the more you stretch it (more displacement), the harder it pulls back (more acceleration). When the mass is at the center (zero displacement), the spring isn&#8217;t pulling at all, so the acceleration is zero.<\/p>\n\n\n\n<p>Because &#8216;a&#8217; is never constant in SHM, you simply can&#8217;t plug it into v = u + at<strong>. We need a new set of tools.<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">The Story of a Breakthrough: How We Cracked the Code<\/h3>\n\n\n\n<p>Understanding SHM wasn&#8217;t a single &#8220;Eureka!&#8221; moment. It was a journey of discovery by some of history&#8217;s greatest scientific minds.<\/p>\n\n\n\n<div class=\"wp-block-group alignfull is-content-justification-center\" style=\"margin-top:0;margin-bottom:0;padding-top:calc( 0.5 * var(--wp--style--root--padding-right, var(--wp--custom--gap--horizontal)));padding-right:var(--wp--style--root--padding-right, var(--wp--custom--gap--horizontal));padding-bottom:calc( 0.5 * var(--wp--style--root--padding-right, var(--wp--custom--gap--horizontal)));padding-left:var(--wp--style--root--padding-left, var(--wp--custom--gap--horizontal))\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-container-core-group-is-layout-b073b61b wp-block-group-is-layout-constrained\">\n<div style=\"height:calc( 0.25 * var(--wp--style--root--padding-right, var(--wp--custom--gap--horizontal)))\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<div class=\"wp-block-columns alignwide are-vertically-aligned-center is-layout-flex wp-container-core-columns-is-layout-6aa4370a wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" width=\"1024\" height=\"631\" src=\"https:\/\/ibphysicswithrao.com\/home\/wp-content\/uploads\/2025\/10\/galileo-pendulum-1024x631.jpg\" alt=\"\" class=\"wp-image-852\" srcset=\"https:\/\/ibphysicswithrao.com\/home\/wp-content\/uploads\/2025\/10\/galileo-pendulum-1024x631.jpg 1024w, https:\/\/ibphysicswithrao.com\/home\/wp-content\/uploads\/2025\/10\/galileo-pendulum-300x185.jpg 300w, https:\/\/ibphysicswithrao.com\/home\/wp-content\/uploads\/2025\/10\/galileo-pendulum-768x473.jpg 768w, https:\/\/ibphysicswithrao.com\/home\/wp-content\/uploads\/2025\/10\/galileo-pendulum-600x370.jpg 600w, https:\/\/ibphysicswithrao.com\/home\/wp-content\/uploads\/2025\/10\/galileo-pendulum.jpg 1050w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\">\n<h2 class=\"wp-block-heading alignwide\">Galileo&#8217;s Experiment:<\/h2>\n\n\n\n<p>While sitting in a cathedral, Galileo noticed a lamp swinging [1<sup data-fn=\"89c57b50-36b4-4662-9711-8a2e25e0165b\" class=\"fn\"><a href=\"#89c57b50-36b4-4662-9711-8a2e25e0165b\" id=\"89c57b50-36b4-4662-9711-8a2e25e0165b-link\">1<\/a><\/sup>]. Using his own pulse as a timer, he was amazed to find that each complete swing took the same amount of time, no matter how wide or narrow the swing was (for small angles). This told him there was a consistent rhythm, a <strong>constant period<\/strong>, to this motion.<\/p>\n<\/div>\n<\/div>\n\n\n\n<div style=\"height:calc( 0.25 * var(--wp--style--root--padding-right, var(--wp--custom--gap--horizontal)))\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group alignfull is-content-justification-center\" style=\"margin-top:0;margin-bottom:0;padding-top:calc( 0.5 * var(--wp--style--root--padding-right, var(--wp--custom--gap--horizontal)));padding-right:var(--wp--style--root--padding-right, var(--wp--custom--gap--horizontal));padding-bottom:calc( 0.5 * var(--wp--style--root--padding-right, var(--wp--custom--gap--horizontal)));padding-left:var(--wp--style--root--padding-left, var(--wp--custom--gap--horizontal))\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-container-core-group-is-layout-b073b61b wp-block-group-is-layout-constrained\">\n<div style=\"height:calc( 0.25 * var(--wp--style--root--padding-right, var(--wp--custom--gap--horizontal)))\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<div class=\"wp-block-columns alignwide are-vertically-aligned-center is-layout-flex wp-container-core-columns-is-layout-6aa4370a wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\">\n<h2 class=\"wp-block-heading alignwide\">Hooke&#8217;s Law<\/h2>\n\n\n\n<p> Hooke was obsessed with springs. He discovered a simple but powerful rule now called <strong>Hooke&#8217;s Law<\/strong>: the force a spring uses to pull back is directly proportional to how far you stretch it (<strong>F = -kx<\/strong>). This was the key! He found the mathematical reason for the changing acceleration. More stretch = more force = more acceleration. You can access his original paper at the internet archive [2<sup data-fn=\"75ae948c-937f-4456-854d-239fb32a5931\" class=\"fn\"><a href=\"#75ae948c-937f-4456-854d-239fb32a5931\" id=\"75ae948c-937f-4456-854d-239fb32a5931-link\">2<\/a><\/sup>]<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full is-resized\"><img decoding=\"async\" width=\"434\" height=\"554\" src=\"https:\/\/ibphysicswithrao.com\/home\/wp-content\/uploads\/2025\/10\/hooks-papers-1.jpg\" alt=\"\" class=\"wp-image-854\" style=\"width:391px;height:auto\" srcset=\"https:\/\/ibphysicswithrao.com\/home\/wp-content\/uploads\/2025\/10\/hooks-papers-1.jpg 434w, https:\/\/ibphysicswithrao.com\/home\/wp-content\/uploads\/2025\/10\/hooks-papers-1-235x300.jpg 235w\" sizes=\"(max-width: 434px) 100vw, 434px\" \/><\/figure>\n<\/div>\n<\/div>\n\n\n\n<div style=\"height:calc( 0.25 * var(--wp--style--root--padding-right, var(--wp--custom--gap--horizontal)))\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n<\/div><\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>Isaac Newton (Late 1600s):<\/strong> Newton brought it all together. He took his Second Law of Motion (F=ma) and combined it with Hooke&#8217;s Law (F=\u2212kx). <strong>This gave birth to the master equation of SHM: ma = -kx. <\/strong>This equation officially proved that acceleration (a) is not constant\u2014it&#8217;s directly proportional to displacement (x). With his invention of calculus, Newton was able to solve this equation, giving us a whole new way to describe motion.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">The New Toolkit: Understanding Path and Phase<\/h3>\n\n\n\n<p>Solving Newton&#8217;s master equation gives us a beautiful, wavy solution that looks like this:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"240\" height=\"52\" src=\"https:\/\/ibphysicswithrao.com\/home\/wp-content\/uploads\/2025\/10\/image-6.png\" alt=\"\" class=\"wp-image-855\"\/><\/figure><\/div>\n\n\n<p>This might look complicated, but it introduces three powerful new concepts that perfectly describe SHM:<\/p>\n\n\n\n<ol start=\"1\" class=\"wp-block-list\">\n<li><strong>Amplitude (A):<\/strong> This is simply the maximum displacement from the center point. It defines the size of the oscillation&#8217;s <strong>path<\/strong>. If you pull a spring 10 cm before letting go, its amplitude is 10 cm.<\/li>\n\n\n\n<li><strong>Angular Frequency (omega):<\/strong> This tells you how quickly the object oscillates. A higher omega means a faster back-and-forth motion.<\/li>\n\n\n\n<li><strong>Phase (phi):<\/strong> This is the most important new idea. Phase tells you the starting point of the object in its cycle. Did it start at the maximum stretch? Or was it already moving through the equilibrium point? This is crucial for comparing the motion of two different oscillators.<\/li>\n<\/ol>\n\n\n\n<p>This new language helps us solve problems that the old equations couldn&#8217;t touch. For example, understanding phase is key to answering questions like this:<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p><strong>Video Example:<\/strong> A particle executes simple harmonic oscillations. What is the phase difference between the acceleration and the displacement of the particle?<\/p>\n<\/blockquote>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe title=\"13. A particle executes simple harmonic oscillations. What is the phase difference between the\" width=\"640\" height=\"360\" src=\"https:\/\/www.youtube.com\/embed\/iSjTem7Rqog?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n<\/div><\/figure>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p>Let&#8217;s think about the very heart of Simple Harmonic Motion. An object in SHM is always being pulled back towards its center or equilibrium position. This &#8220;restoring force&#8221; is key. It means the direction of the force is always trying to counteract the object&#8217;s position. This leads to a classic question:<\/p>\n\n\n\n<p><strong> In simple harmonic oscillations which two quantities always have opposite directions?<\/strong><\/p>\n<\/blockquote>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe title=\"12. The motion of an object is described by the equation acceleration \u221d - displacement. what is the\" width=\"640\" height=\"360\" src=\"https:\/\/www.youtube.com\/embed\/gfIsgk5JmiU?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n<\/div><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Why Does This Matter? SHM is Everywhere!<\/h3>\n\n\n\n<p>Understanding SHM isn&#8217;t just for passing exams; it&#8217;s fundamental to how the universe works.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Waves:<\/strong> All waves\u2014sound, light, water\u2014are essentially made of countless tiny oscillators working together.<\/li>\n\n\n\n<li><strong>Engineering:<\/strong> Engineers use SHM principles to design buildings that can withstand earthquakes and car suspensions that give you a smooth ride.<\/li>\n\n\n\n<li><strong>Technology:<\/strong> The quartz crystal in your watch and the circuits in your phone that tune into radio signals all rely on precise electronic oscillators.<\/li>\n\n\n\n<li><strong>Music:<\/strong> Every musical note is a combination of vibrations (oscillations) traveling through the air as sound waves.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">A Final Thought: Don&#8217;t Fear &#8220;Failed&#8221; Equations<\/h3>\n\n\n\n<p>In TOK, we learn that scientific models are not reality itself; they are simplified maps designed for a specific purpose. <em>The fact that your trusty kinematics equations\u2014a powerful <strong>model<\/strong> for constant acceleration\u2014don&#8217;t work for SHM isn&#8217;t a failure. Instead, it&#8217;s a discovery of the model&#8217;s <strong>scope and limitations<\/strong><\/em>. \ud83d\uddfa\ufe0f<\/p>\n\n\n\n<p>This moment is an invitation to ask a classic <strong>knowledge question<\/strong>: <em>To what extent does the failure of a scientific model contribute to the growth of knowledge?<\/em> This situation perfectly demonstrates a core principle of the Natural Sciences as an <strong>Area of Knowledge (AOK)<\/strong>: knowledge progresses not by proving things right, but by finding out where our current understanding is wrong. These &#8220;failures&#8221; are the catalysts for creating more comprehensive and powerful models.<\/p>\n\n\n\n<p>So, as a <strong>knower<\/strong>, embrace these moments. When a problem doesn&#8217;t fit your initial framework, it&#8217;s not a dead end. It\u2019s a sign that you are moving from a simple map to a more detailed one, pushing the boundaries of both your <strong>personal and shared knowledge<\/strong>. Keep questioning your assumptions, keep challenging your models, and keep exploring the rich complexity of the universe. \ud83e\udd14<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Bibliography:<\/h2>\n\n\n<ol class=\"wp-block-footnotes\"><li id=\"89c57b50-36b4-4662-9711-8a2e25e0165b\"><a href=\"https:\/\/richardnilsen.com\/2022\/09\/04\/alphabestiary-g-galileo-galilei\/\">https:\/\/richardnilsen.com\/2022\/09\/04\/alphabestiary-g-galileo-galilei\/<\/a> <a href=\"#89c57b50-36b4-4662-9711-8a2e25e0165b-link\" aria-label=\"Jump to footnote reference 1\">\u21a9\ufe0e<\/a><\/li><li id=\"75ae948c-937f-4456-854d-239fb32a5931\"><a href=\"https:\/\/archive.org\/details\/bim_early-english-books-1641-1700_lectures-de-potentia-res_hooke-robert_1678\">https:\/\/archive.org\/details\/bim_early-english-books-1641-1700_lectures-de-potentia-res_hooke-robert_1678<\/a> <a href=\"#75ae948c-937f-4456-854d-239fb32a5931-link\" aria-label=\"Jump to footnote reference 2\">\u21a9\ufe0e<\/a><\/li><\/ol>","protected":false},"excerpt":{"rendered":"<p>When Your Go-To Equations Give Up Think about the world around you: a pendulum swinging in a clock, a guitar string vibrating to make a note, or even a bungee jumper bouncing up and down. These are all examples of a special kind of rhythmic motion called Simple Harmonic Motion (SHM). In your physics class, you&#8217;ve probably become good friends with the kinematics equations: These equations are fantastic for figuring out the motion of a ball thrown in the air or a car accelerating down a road. But here\u2019s the puzzle: the moment you try to use them on a swinging pendulum or a bouncing spring, they completely fail. Why do these powerful tools fall silent when faced with the simple, repeating dance of SHM? Let&#8217;s find out. The Core Problem: A Constantly Changing Acceleration The kinematics equations you know and love have one critical weakness: they only work when acceleration is constant. For SHM, acceleration is the exact opposite\u2014it&#8217;s always changing! This leads to one of the most common misconceptions. Consider a typical exam question from one of our videos: The acceleration of the object is always proportional to its displacement, and it points in the opposite direction. Think of a spring: the more you stretch it (more displacement), the harder it pulls back (more acceleration). When the mass is at the center (zero displacement), the spring isn&#8217;t pulling at all, so the acceleration is zero. Because &#8216;a&#8217; is never constant in SHM, you simply can&#8217;t plug it into v = u + at. We need a new set of tools. The Story of a Breakthrough: How We Cracked the Code Understanding SHM wasn&#8217;t a single &#8220;Eureka!&#8221; moment. It was a journey of discovery by some of history&#8217;s greatest scientific minds. Galileo&#8217;s Experiment: While sitting in a cathedral, Galileo noticed a lamp swinging [1]. Using his own pulse as a timer, he was amazed to find that each complete swing took the same amount of time, no matter how wide or narrow the swing was (for small angles). This told him there was a consistent rhythm, a constant period, to this motion. Hooke&#8217;s Law Hooke was obsessed with springs. He discovered a simple but powerful rule now called Hooke&#8217;s Law: the force a spring uses to pull back is directly proportional to how far you stretch it (F = -kx). This was the key! He found the mathematical reason for the changing acceleration. More stretch = more force = more acceleration. You can access his original paper at the internet archive [2] Isaac Newton (Late 1600s): Newton brought it all together. He took his Second Law of Motion (F=ma) and combined it with Hooke&#8217;s Law (F=\u2212kx). This gave birth to the master equation of SHM: ma = -kx. This equation officially proved that acceleration (a) is not constant\u2014it&#8217;s directly proportional to displacement (x). With his invention of calculus, Newton was able to solve this equation, giving us a whole new way to describe motion. The New Toolkit: Understanding Path and Phase Solving Newton&#8217;s master equation gives us a beautiful, wavy solution that looks like this: This might look complicated, but it introduces three powerful new concepts that perfectly describe SHM: This new language helps us solve problems that the old equations couldn&#8217;t touch. For example, understanding phase is key to answering questions like this: Video Example: A particle executes simple harmonic oscillations. What is the phase difference between the acceleration and the displacement of the particle? Let&#8217;s think about the very heart of Simple Harmonic Motion. An object in SHM is always being pulled back towards its center or equilibrium position. This &#8220;restoring force&#8221; is key. It means the direction of the force is always trying to counteract the object&#8217;s position. This leads to a classic question: In simple harmonic oscillations which two quantities always have opposite directions? Why Does This Matter? SHM is Everywhere! Understanding SHM isn&#8217;t just for passing exams; it&#8217;s fundamental to how the universe works. A Final Thought: Don&#8217;t Fear &#8220;Failed&#8221; Equations In TOK, we learn that scientific models are not reality itself; they are simplified maps designed for a specific purpose. The fact that your trusty kinematics equations\u2014a powerful model for constant acceleration\u2014don&#8217;t work for SHM isn&#8217;t a failure. Instead, it&#8217;s a discovery of the model&#8217;s scope and limitations. \ud83d\uddfa\ufe0f This moment is an invitation to ask a classic knowledge question: To what extent does the failure of a scientific model contribute to the growth of knowledge? This situation perfectly demonstrates a core principle of the Natural Sciences as an Area of Knowledge (AOK): knowledge progresses not by proving things right, but by finding out where our current understanding is wrong. These &#8220;failures&#8221; are the catalysts for creating more comprehensive and powerful models. So, as a knower, embrace these moments. When a problem doesn&#8217;t fit your initial framework, it&#8217;s not a dead end. It\u2019s a sign that you are moving from a simple map to a more detailed one, pushing the boundaries of both your personal and shared knowledge. Keep questioning your assumptions, keep challenging your models, and keep exploring the rich complexity of the universe. \ud83e\udd14 Bibliography:<\/p>\n","protected":false},"author":1,"featured_media":856,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":"[{\"content\":\"<a href=\\\"https:\/\/richardnilsen.com\/2022\/09\/04\/alphabestiary-g-galileo-galilei\/\\\">https:\/\/richardnilsen.com\/2022\/09\/04\/alphabestiary-g-galileo-galilei\/<\/a>\",\"id\":\"89c57b50-36b4-4662-9711-8a2e25e0165b\"},{\"content\":\"<a href=\\\"https:\/\/archive.org\/details\/bim_early-english-books-1641-1700_lectures-de-potentia-res_hooke-robert_1678\\\">https:\/\/archive.org\/details\/bim_early-english-books-1641-1700_lectures-de-potentia-res_hooke-robert_1678<\/a>\",\"id\":\"75ae948c-937f-4456-854d-239fb32a5931\"}]"},"categories":[1],"tags":[26,30,29,27,28],"class_list":["post-850","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-blog","tag-ibdp-physics","tag-rathankar-com","tag-shm","tag-theory-of-knowledge-examples","tag-tok-exhibits"],"_links":{"self":[{"href":"https:\/\/ibphysicswithrao.com\/home\/wp-json\/wp\/v2\/posts\/850","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ibphysicswithrao.com\/home\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/ibphysicswithrao.com\/home\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/ibphysicswithrao.com\/home\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/ibphysicswithrao.com\/home\/wp-json\/wp\/v2\/comments?post=850"}],"version-history":[{"count":2,"href":"https:\/\/ibphysicswithrao.com\/home\/wp-json\/wp\/v2\/posts\/850\/revisions"}],"predecessor-version":[{"id":858,"href":"https:\/\/ibphysicswithrao.com\/home\/wp-json\/wp\/v2\/posts\/850\/revisions\/858"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/ibphysicswithrao.com\/home\/wp-json\/wp\/v2\/media\/856"}],"wp:attachment":[{"href":"https:\/\/ibphysicswithrao.com\/home\/wp-json\/wp\/v2\/media?parent=850"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ibphysicswithrao.com\/home\/wp-json\/wp\/v2\/categories?post=850"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ibphysicswithrao.com\/home\/wp-json\/wp\/v2\/tags?post=850"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}