Why Oscillators are Key to Differential Equations

Comments · 127

• DI

  @dibeos · 6 months ago (edited) · pinned

  This PDF is the result of compressing hundreds of hours of research into the main oscillators studied via differential equations: <br><br><a href="https://dibeos.com/wp-content/uploads/2026/03/the_main_oscillators_in_differential_equations__free-1.pdf">https://dibeos.com/wp-content/uploads/2026/03/the_main_oscillators_in_differential_equations__free-1.pdf</a>

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• WH

  @whoknowsnubby · 6 months ago

  My guess was distance term squared is always positive, distance term cubed preserves signs, having +/- in distance term suggests oscillation.

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• DO

  @doctor_no_ · 6 months ago

  I found the correct equation by noticing that in a Taylor expansion of a small force, x^3 is the next term you can use (if you want) after the linear x term. Also, x^3 is an odd function hence it always wants to bring the object to the equilibrium position. The x^2 equation will want to keep making the object go far from equilibrium. What do I win? God I want to go back to my studies and research :(

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• AR

  @artscience9981 · 6 months ago

  I love the way you use physical modeling to give intuition for how the equations work!

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• TW

  @twow5578 · 6 months ago

  You guys are absolutely amazing.<br>I&apos;m a mathematician at heart, but lately I was kinda forced to take a course in physics, having no former background in the subject, and even though I&apos;ve been playing with differential equations for ages, only today I learned about simple harmonic oscillation, and its derivation looked simple and boring enough to me so I continued, but exactly as I finished I saw this video and it really expanded the topic for me. Perfect timing and perfect video, I love your work

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• SW

  @SwaltyPhysics · 2 months ago

  Nice job. I will add this link to my video, section &quot;Any oscillator in the world&quot;.

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• HE

  @heartstopper-x · 6 months ago

  You should mention the Duffing oscillator, which is just a general combination of the damped, forced and anharmonic oscillators.

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• DO

  @dopamine_mein_doobaa · 6 months ago

  After having watched this video, I do not regret pursuing electrical engineering.

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• JM

  @jmcsquared18 · 6 months ago

  We cover this in lab next Tuesday. I try to get the engineers to see, a pendulum and a spring are the same system: perturbed equilibria with restoring forces. <br><br>When linearized, they produce the exact same differential equation for small amplitudes. Which shows they very much are controlled by the same physics.

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• KH

  @KhalilEstell · 6 months ago

  Oh wow I got the answer right by considering how the acceleration would change based on the position and how x^3 retains its sign.<br><br>Thank you so much for this video. I&apos;ve been starting my journey of learning math again after 9 years from university and these have been so helpful. And thank you for making such high quality learning material.

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• BC

  @BCarli1395 · 6 months ago

  Very good videos with supplemental pdf’s—you guys provide a valuable service to those learning STEM subjects. Thank you. I wish this had been available fifty years ago. 😊

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• BE

  @beanieredd-iu4xg · 6 months ago

  This is a very good and intuitive video. &nbsp;I particularly like the slider presentation of the family of equations.