# Questions tagged [approximations]

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### Hooke's full unapproximated law

It is known that the Hooke's law relating the restoring force of a spring to the distance of retraction from the equilibrium position, is only an approximation. That is, the equation $F=-kx$ is only ...
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### Why is a particle non-relativistic when its kinetic energy is small compared to its rest energy?

For example, nucleons in nucleus are in motion with kinetic energies of 10 MeV. Their rest energies are about 1000 MeV. Kinetic energy of nucleons is small compared to rest energy. They are hence ...
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### How do we understand the results of $1/N$ or $\epsilon$ expansion beyond leading orders?

When we do $1/N$ expansions in, say, 2+1$D$ $O(N)$ models and try to extract all kinds of critical exponents from it, we get the following results for the scaling dimensions of various operators up to ...
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### The reasoning behind doing series expansions and approximating functions in physics

It is usual in physics, that when we have a variable that is very small or very large we do a power series expansion of the function of that variable, and eliminate the high order terms, but my ...
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### Small Angle Approximation for Simple Pendulum

I am working on a simple pendulum problem. The $y$ direction is vertical and the $x$ direction is horizontal. Displacement in the $x$ direction is taken to be much less than the length of the string, ...
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### Criteria on good inertial system approximation

I'm currently wrapping my head around Newton's First Law. I think I start to get a basic understanding on the meaning of this law in terms of "the existence of inertial system". Basically my ...
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### Series expansion of $N$-particle potential energy

I am trying to understand the so-called Taylor expansion (or series expansion) of potential energy of a system of $N$-particles. This expanded form is stated without derivation in some molecular ...
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### How to interpret results of stationary phase approximation in GW case?

As time increases, the amplitude and frequency of the GW signal also increase. But after using the stationary phase approximation, the signal is proportional to ${1/f^{7/6}}$, where $f$ is the GW ...
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### Capacitor demo explanation

I know that for a charged capacitor as one separates the plates further apart the voltage increases while the capacitance decreases. But surely as the plates are pulled further and further apart the ...
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### Theoretical definition and pratical mesurement of differential cross section

In Sakurai's book, the definition of differential cross section is: $$d\sigma/d\Omega= transition \;rate / probability\; flux$$ However this def doesn't contain any information about the thickness ...
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### Oscillator with decaying restoring force

Suppose a system that is described by the equation of motion: $$\ddot{x} = -k\cdot x\cdot \exp\left(-\frac{t^2}{2\sigma^2}\right).$$ (For example a spring with decaying stiffness.) I'd like to ...
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### Models in physics [closed]

As I said in another question I am just a physics enthusiast so I am sorry for my very poor knowledge. What is meant by models in physics? what is their function and why physicists imply them? Are ...
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### How can I Derive the Equation for Coefficient of Linear Thermal Expansion?

I know the relationship between change in temperature and change in length. When the ambient temperature around any substance is increased, its length increases. This is due to molecules gaining more ...
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### Why does Coulomb's law hold only for two point charges? [closed]

What is the condition for validation of Coulomb's Law?
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### Is the harmonic oscillator approximation valid in occasion of very powerful fields?

I noted that in physics, to study electromagnetic wave phenomena when there is a sinusoidal behaviour, often is used the approximation of harmonic oscillation. I tried to understand the basics of why ...
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### Is continuum mechanics a generalization or an approximation to point particle mechanics?

Newtonian Mechanics is usually presented as a theory of point particles (and forces). My impression of the status of continuum mechanics is that it is mostly taken as an approximate description for ...
I saw another question which says the speed of light is "$3\times 10^8 \:\rm m/s$", and I know that the speed of light is $299,792,458\ \rm m/s$. My chemistry teacher taught me that $3.0$ means $3.0 \... 1answer 184 views ### Kepler's Second Law: Why do we calculate the area of a triangle rather than the area of a sector? Kepler's Second Law states that equal areas are swept in equal times. When calculating this area, why do we use the formula for the area of a triangle rather than the area of a sector? 2answers 511 views ### Path difference in double slit experiment Generally the path difference between two rays is considered as dsin$\theta and for this generally the two rays are considered parallel. That is shown in diagram 'c'. My questions - 1. is even ...
At the end he concludes $V(x) = V''(x_0)(x-x_0)^2$. How does he get to know that the rest are $0$? How does he conclude $V''(x_0) = k$. Please try to explain in easy ways and tough vocabulary. I don't ...