All Questions
Tagged with applications physics
67
questions
2
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0
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76
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whats is the applications of the minimization of eigenvalue in the real life ( physics,the natural sciences...)
let $\lambda_{1}(\Omega),\lambda{2}(\Omega),\lambda_{3}(\Omega)...$ the eigenvlues of the laplacian Operator with Dirichlet condition on the boundary on $\Omega $
the classical spectrale optimisation ...
- 704
1
vote
0
answers
117
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Physical meaning of this boundary value differential equation
I am considering the following boundary value problem:
$$-\frac{\mathrm{d}}{\mathrm{d}x} \left[ a(x) \frac{\mathrm{d}}{\mathrm{d}x}(u(x)) \right] + c(x)u(x) = f(x),$$
where $x \in [0,1]$ and $u(0) = ...
- 3,993
9
votes
1
answer
132
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How many times do you have go back and forth to get out of a deadlock?
Here's a challenging question for you math lovers.
This question was originally asked in Physics SE but I was suggested to post it here.( You can see it here.)
Many a times we have been inside a ...
user504401
2
votes
2
answers
252
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Probability density for velocity in mechanical energy
To be sure my basic physics isn't rusty...
Consider a 2-D bowled shaped classical potential well within which a classical particle of mass m is rolling.
In this system the conservation of energy ...
- 6,343
2
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2
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1k
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Prove $v = \sqrt{\frac{2gRh}{R + h}}$ from Given (below)
Given:
$$F = \frac{mgR^2}{(x + R)^2}$$
$m = \text{mass}$
$g = \text{Acceleration due to gravity}$
$x = x(t)$ is the object's distance above the surface at time $t$.
I believe this is the ...
- 141
1
vote
1
answer
7k
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Hydrostatic force problem with trapezoids?
If I have a trapezoid with a $4$m and $8$m base that is partly submerged vertically in water so that the top is $2$m above the surface and the bottom is $2$m below the surface; how do I express the ...
- 575
0
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1
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UNRESOLVED: Pushing oil out of a tank using work integration
I have a tank of oil with a density of $900\frac{kg}{m^3}$. My tank has a spout that is $2$ meters tall and the general radius of the tank is $6$ meters. It is half full of oil and I want to find the ...
- 575
0
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1
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112
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How to show something does not vary with time?
Consider a glider flying at velocity $\bf u$ (giving $u = |\bf u| $ on its speedometer) at an angle $θ ∈ (−π, π]$ to the horizon.
Positive angle $θ ∈ (0, π/2)$ coincides with the glider’s nose ...
- 145
0
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2
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1k
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Tacoma Narrows bridge collapse : mathematical explanation. [closed]
What is the exact mathematical reason behind the Tacoma narrow bridge collapse ?
I have googled about the collapse , but I didn't get a correct reason and a mathematical model.
- 73
6
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1
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Applications of group theory to classical mechanics
Today, a friend and I solved a classical mechanics problem using group theory. The problem was the following:
Around a circumference, there are $N$ children evenly spaced. In the center, there is a ...
- 2,965
8
votes
1
answer
360
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How can one tell if a PDE describes wave behaviour?
I have been looking at a lot of different non-linear PDEs which describe waves lately and have come to the realisation that I don't know what it is about these PDEs that make them behave like waves. ...
- 93
1
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0
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80
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Heat problem with an internal source of heat for which the maximum principle doesn't hold.
Heat problem with an internal source of heat for which the maximum principle doesn't hold. The problem is the following and honestly I don't know how to solve it...
$$u_{t}=u_{tt}+2(t+1)+x(1-x) , 0&...
- 3,766
3
votes
1
answer
5k
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Applied Mathematics: Spherical Polar Coordinates and Newton's Second Law
I've been attempting this question but can't seem to find a solution.
Question:
A particle of mass $m$ moves under the influence of a force which, in spherical polar coordinates, only acts in the ...
- 455
0
votes
1
answer
46
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Locus Equation $f(r) = \frac{-h^2}{r^3}$?
For the Locus equation
$$\frac{\mathrm{d^2}u }{\mathrm{d} \theta^2} + u = - \frac{1}{h^2u^2}f\left(\frac{1}{u} \right )$$
How do I find the solution for $f(r)= \frac{-h^2}{r^3}$ and sketch the ...
- 455
1
vote
1
answer
224
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When is $0$ ever used in real life?
I've just been going through an equation, which is as follows:
$(x+4)^2 = 16$
Lets work through it:
$$x^2 + 8x +16 = 16$$
$$x^2 +8x = 0$$
$$x^2 = -8x$$
$$x = -8$$
However, as i've just found ...
- 2,110