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#potentialenergy — Public Fediverse posts

Live and recent posts from across the Fediverse tagged #potentialenergy, aggregated by home.social.

  1. A cycloidal pendulum - one suspended from the cusp of an inverted cycloid - is isochronous, meaning its period is constant regardless of the amplitude of the swing. Please find the proof using energy methods: Lagrange's equations (in the images attached to the reply).

    Background:
    The standard pendulum period of \(2\pi\sqrt{L/g}\) or frequency \(\sqrt{g/L}\) holds only for small oscillations. The frequency becomes smaller as the amplitude grows. If you want to build a pendulum whose frequency is independent of the amplitude, you should hang it from the cusp of a cycloid of a certain size, as shown in the gif. As the string wraps partially around the cycloid, the effect decreases the length of the string in the air, increasing the frequency back up to a constant value.

    In more detail:
    A cycloid is the path taken by a point on the rim of a rolling wheel. The upside-down cycloid in the gif can be parameterized by \((x, y)=R(\theta-\sin\theta, -1+\cos\theta)\), where \(\theta=0\) corresponds to the cusp. Consider a pendulum of length \(L=4R\) hanging from the cusp, and let \(\alpha\) be the angle the string makes with the vertical, as shown (in the proof).

    #Pendulum #Cycloid #Period #Frequency #SHM #TimePeriod #CycloidalPendulum #Lagrange #Cusp #Energy #KineticEnergy #PotentialEnergy #Lagrangian #Length #Math #Maths #Physics #Mechanics #ClassicalMechanics #Amplitude #CircularFrequency #Motion #Vibration #HarmonicMotion #Parameter #ParemeterizedEquation #GoverningEquations #Equation #Equations #DifferentialEquations #Calculus

  2. A cycloidal pendulum - one suspended from the cusp of an inverted cycloid - is isochronous, meaning its period is constant regardless of the amplitude of the swing. Please find the proof using energy methods: Lagrange's equations (in the images attached to the reply).

    Background:
    The standard pendulum period of \(2\pi\sqrt{L/g}\) or frequency \(\sqrt{g/L}\) holds only for small oscillations. The frequency becomes smaller as the amplitude grows. If you want to build a pendulum whose frequency is independent of the amplitude, you should hang it from the cusp of a cycloid of a certain size, as shown in the gif. As the string wraps partially around the cycloid, the effect decreases the length of the string in the air, increasing the frequency back up to a constant value.

    In more detail:
    A cycloid is the path taken by a point on the rim of a rolling wheel. The upside-down cycloid in the gif can be parameterized by \((x, y)=R(\theta-\sin\theta, -1+\cos\theta)\), where \(\theta=0\) corresponds to the cusp. Consider a pendulum of length \(L=4R\) hanging from the cusp, and let \(\alpha\) be the angle the string makes with the vertical, as shown (in the proof).

    #Pendulum #Cycloid #Period #Frequency #SHM #TimePeriod #CycloidalPendulum #Lagrange #Cusp #Energy #KineticEnergy #PotentialEnergy #Lagrangian #Length #Math #Maths #Physics #Mechanics #ClassicalMechanics #Amplitude #CircularFrequency #Motion #Vibration #HarmonicMotion #Parameter #ParemeterizedEquation #GoverningEquations #Equation #Equations #DifferentialEquations #Calculus

  3. CW: Love / Care in Climate Change messages...

    Caring for kids and communities seems to work as topics to talk about, and goes across all countries, generations, genders, political ideologies.

    More than any number or money in the middle between us, talking about more-human things is well. much more human. Other things can make us more angry or bitter because they are much less human or even self-sabotage (like money between us - inflation, false valuation, things just bought, rented and sold- as property not really cared for).
    ============
    Summary:
    ============
    We might get angry or misunderstand but doing what we can for love and caring covers a broad range of emotions... if it's "A Better Place for us / them / the children"

    Time 44m01s of #Ep228 #TransitionShow #Quote / @TransitionShow

    #Podcast Post: mastodon.energy/@TransitionSho

    ====================

    #Motivation #Love #Change #Communication #BetterPlace
    #Abundance of #Love
    #PotentialEnergy + #FreeSchool

    #ThinkAboutTheChildren #ProtectWhatWeLove
    #ClimateChange

    #Green #Energy #GreenAgenda
    #Value #Value4Value #V4V

  4. CW: Love as a better framing for change?...

    #Question If Love is such an clearly outstanding frame with which to proceed, then do you have a theory about why we don't see it being used more?

    From people saying "Doom" to
    more people saying "Love?"....

    Time 50mins of #Ep228 #TransitionShow #Quote / @TransitionShow

    #Podcast Post here: mastodon.energy/@TransitionSho

    ====================
    Why don't we see Love used
    more as a frame?
    ====================

    My first sniper instinct says "People care more for profit than people or environment, that's why" which is highly true or indisputable.

    Love is maybe not used in a y intellectual sectors like #STEM, #government, #politicians and the related #mainstream bubbles.

    #Scientist are trusted to some extent (but also people over-bombarded) but are also often dispassionate with too much information unrelated to almost anyone.

    Baking it into policy is perhaps near impossible and politicians just use it to sell themselves into their next career... rather than anyone ever implement an industry that relies on "this is how it is now" and will be forever if they want to keep power and profit as maximised as possible.

    ====================

    #Motivation #Love #Change #Communication #BetterPlace
    #Abundance of #Love
    #PotentialEnergy + #FreeSchool

    #ThinkAboutTheChildren #ProtectWhatWeLove
    #ClimateChange

    #Green #Energy #GreenAgenda
    #Value #Value4Value #V4V

  5. 💥 thekidshouldseethis.com/post/p

    From the American Journal of #Physics: "When weaving the chain, one realizes that a large #potentialenergy is stored in the sticks, and the ends of the chain must be held still by using a weight or one’s hand… When one end of the chain is released, the so-called ‘#stickbomb’ detonates—the potential energy is released as the sticks pop up and a traveling #wave is formed…”

    #video #chainreaction #domino #popsiclesticks #science #activities #play #hevesh5 #compilation

  6. 💥 thekidshouldseethis.com/post/p

    From the American Journal of #Physics: "When weaving the chain, one realizes that a large #potentialenergy is stored in the sticks, and the ends of the chain must be held still by using a weight or one’s hand… When one end of the chain is released, the so-called ‘#stickbomb’ detonates—the potential energy is released as the sticks pop up and a traveling #wave is formed…”

    #video #chainreaction #domino #popsiclesticks #science #activities #play #hevesh5 #compilation

  7. 💥 thekidshouldseethis.com/post/p

    From the American Journal of #Physics: "When weaving the chain, one realizes that a large #potentialenergy is stored in the sticks, and the ends of the chain must be held still by using a weight or one’s hand… When one end of the chain is released, the so-called ‘#stickbomb’ detonates—the potential energy is released as the sticks pop up and a traveling #wave is formed…”

    #video #chainreaction #domino #popsiclesticks #science #activities #play #hevesh5 #compilation

  8. 💥 thekidshouldseethis.com/post/p

    From the American Journal of #Physics: "When weaving the chain, one realizes that a large #potentialenergy is stored in the sticks, and the ends of the chain must be held still by using a weight or one’s hand… When one end of the chain is released, the so-called ‘#stickbomb’ detonates—the potential energy is released as the sticks pop up and a traveling #wave is formed…”

    #video #chainreaction #domino #popsiclesticks #science #activities #play #hevesh5 #compilation

  9. 💥 thekidshouldseethis.com/post/p

    From the American Journal of #Physics: "When weaving the chain, one realizes that a large #potentialenergy is stored in the sticks, and the ends of the chain must be held still by using a weight or one’s hand… When one end of the chain is released, the so-called ‘#stickbomb’ detonates—the potential energy is released as the sticks pop up and a traveling #wave is formed…”

    #video #chainreaction #domino #popsiclesticks #science #activities #play #hevesh5 #compilation

  10. Companies Have New Take on Old Energy Storage Tech - According to Spectrum, several companies are poised to make a splash storing energy with gravity. ... - hackaday.com/2021/01/07/compan #potentialenergy #energystorage #greenhacks #gravity