# Questions tagged [approximations]

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### How is Schwarzschild metric asymptotically flat for large $r$?

The Schwarzschild line element is: $$ds^2 = -\left(1-\frac{2M}{r}\right)dt^2 + \left(1-\frac{2M}{r}\right)^{-1}dr^2 +r^2(d\theta^2 +\sin^2\theta d\phi^2).$$ As $r \to \infty$, this is supposed to ...
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### What is the Difference between $F = mg$ and law of universal gravitation? [duplicate]

is (F=mg) equal to (F=GmM/r^2)? And what's the difference between them?
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### Is spring constant really a constant value? ( Assume the spring is not changed )

l just encountered a problem that is about a string in harmonic motion. The question states that the cord is elastic and gives a table like this The question didn't states that the cord changes, only ...
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### Why it is not possible to get exact solution for cubic potential perturbation for 1D SHO and we have to use perturbation theory? [duplicate]

Can anyone help me in providing the process of finding exact solution in case of cubic perturbation in 1D SHO, or any suitable resource?
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### Why it is not possible to get exact solution for cubic potential perturbation in 1D SHO and we have to use perturbation theory?

For $x$ and $x^2$ we get exact solution easily without applying perturbation theory, but I read that above order perturbation can not be solved exactly. Can anyone explain clearly why?
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### Can we ignore air resistance?

Is there any case in real life we can get the right (correct) "equations of motion" for object with ignoring air resistance? In any object condition (size or shape of the object we are studying).
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### When can a function $f(x_0 - x)$ be approximated as $f(x_0 - x) = f(x_0) - f'(x_0) x$?

When can a function $f(x_0 - x)$ be approximated as $f(x_0 - x) = f(x_0) - f'(x_0) x$? In Reif's statistical mechanics it is said that when $x$ is much smaller than $x_0$ then the approximation can be ...
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### Phase-ordering dynamics: numerical solution of the Mazenko equation in $D=2$

I'm considering the Mazenko equation as it's written in https://doi.org/10.1103/PhysRevB.46.10594 (eq. 7) \begin{equation} \label{a} f''+\left(\frac{1}{x}+\frac x 4 \right)f'+\frac \lambda \pi \,\tan\...
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### Simple harmonic motion amplitude of oscillation

I know that for a pendulum we need small amplitudes. But why is it necessary that a spring oscillator should have small amplitude of oscillation?
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### When is a parameter considered small for perturbation and how does physical units affect that?

In perturbation theory procedures (not specific to any particular topic) we tend to have (or delibrately insert) some small variable $\epsilon$ in an equation that is otherwise difficult to solve if ...
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### Derivation of Commutators for Galillean Transformations in Ballentine

I am trying to follow along the derivation of the commutator relations for the generators of the Galilei Group in Ballentine. He states that the product of two infinitesimal generators and their ...
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### Change in areal element

I am reading Griffith's Introduction to Electrodynamics., On example 1.7 while calculating surface integral of $x = 2$ for a cube of side 2., the book states $da = dy \cdot dz$ I don't get this, what ...
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### What's the difference between a post-Minkowskian approximation and a post-Newtonian one?

I'm studying the book Gravity by Poisson & Will. Specifically, I'm interested in the post-Newtonian and post-Minkowskian approximations showed in chapters 6-10. The problem I'm having is ...
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