Recent content by haruspex

Have you quoted that correctly? When it contacts the spring, the spring is relaxed, so that is the equilibrium position. Does it perhaps say "moving from the equilibrium position "?

That really does not help much by itself. Please take the trouble to post the working as well, typing the equations in, preferably using LaTeX.

You are entitled to know why. Is it possible to reply to the warning?

Yes, I do realise that. The purpose of my post was to challenge the statement I quoted in post #12 in a way that might convince the errant professor (Methinks s/he doth profess too much). "Consider the case in which …"

Centripetal acceleration is the component of acceleration that is normal to the velocity. If the plane is flying level, its lift is g but its centripetal acceleration is zero.

I'll say it again more strongly. The only reliable way to handle an idealisation is as the limit of realistic versions. When there is more than one parameter to take to a limit, the relative rates of approach can affect the answer. In such cases, the problem is under-determined. See e.g. the...

"An infinite mass is placed on each side of a beam balance. By symmetry, they balance." In the real world, nothing is perfectly symmetrical. Idealisations are only valid if they work as the limit of a sequence of realistic versions; and if multiple limits are involved then it must not matter...

And the one knows what it says anyway, which helps.

I used to think that way, but then along came virtual particles. Those many philosophers who had been unhappy with forces magically acting over arbitrary distances were vindicated. Likewise, GR resolved philosophical objections (Leibniz, Mach) to Newton’s absolute empty space; Bishop Berkeley*...

Which is still illegible.

I am reminded of a bogus calculation by Australian politician Greg Hunt. https://www.abc.net.au/news/2015-10-28/fact-check-direct-action-vs-carbon-tax/6847234 He claimed the previous government's carbon tax had cost $1300 per tonne of reduction. His method was to divide the money companies had...

A vertical stick in the ground would have been good enough for Eratosthenes. Need a plumb line, though. The context is unclear. Are we to assume the tools available to an architect of Stonehenge or to a modern visitor?

According to AI Overview Evaluation:The resulting integral ##\int\sqrt{1+cosh^2(x)}dx## does not have a simple elementary closed-form solution and often requires numerical methods for precise calculation.

If we conclude ##x=a## (where a is well defined) then we necessarily mean that it is the only value of x that satisfies the conditions. This follows from the field axiom I quoted. Given the condition ##x^2=a^2##, we can conclude that ##x\in\{a,-a\}##, not that ##x=a##. This is different from...

Right, which is why it is a fallacy to claim it equals zero. It is an axiom that if x=a and x=b then a=b. That is what would be implied by the statement that the limit equals zero.