Questions related to mathematical physics which include application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and for the formulation of physical theories

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1answer
29 views

Basic expression mangling question

I am looking at the solution of a physics/statistics hybrid exercise, and I can't figure out how one expression step took place. I have that $${dx \over dt} = gt$$ $$T = \sqrt{2h \over g}$$ where $...
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1answer
2k views

Solving differential equation for simple harmonic motion. Finding k?

A 1 lb weight is suspended from a spring. Let y give the deflection (in inches) of the weight from its static deflection position, where “up” is the positive direction for y. If the static deflection is ...
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1answer
3k views

Finding the period and frequency for simple harmonic motion

A 1 lb weight is suspended from a spring. Let y give the deflection (in inches) of the weight from its static deflection position, where “up” is the positive direction for y. If the static deflection is ...
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2answers
951 views

Why are the phase portrait of the simple plane pendulum and a domain coloring of sin(z) so similar?

The simple plane pendulum $$\frac{d^2\theta}{dt^2} + \frac{g}{l}\sin{\theta} = 0$$ has the very perdy phase portrait Meanwhile, a domain coloring of $\sin(z)$ in the complex plane is Why are ...
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0answers
50 views

Solving inverse square of visible scale

I'm not super-adept in mathematics, so I turn to you for help. As I read, the perceived scale of an object reduces by the inverse square as the viewed distance increases. In order to solve for this, ...
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4answers
1k views

Numerical approximation of a complex integral with a nested exponential

I've been working on a maths problem as part of my Physics PhD; but have been stumped by the following integral. All I need to know is a numeric approximation to the integral (along with an estimation ...
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1answer
315 views

Related Rates of perpendicular motion

Two objects A and B are connected by a rigid rod that has a length L. The objects slide along perpendicular guide rails. If A slides to the left with a constant speed v, what is the velocity of B when ...
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0answers
435 views

On the geometric arguments used in Newton's *Principia Mathematica Naturalis Philosophae*

When one reads Newton's Principia Mathematica, one is immediately aware of the complexity of the synthetic geometry that he uses to prove his propositions. This I understand because all of the ...
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1answer
20 views

Simplification of Equation Involving Second Partials

I was reading this article and I'm trying to follow this author's proof. The author jumps from $$\psi_1(x)\frac{\partial^2\psi_2(x)}{\partial x^2}-\psi_2(x)\frac{\partial^2\psi_1(x)}{\partial x^2}=0$$...
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3answers
402 views

Is there a mathematical theory of physical knots?

From the point of view of people tying real knots (canonically, sailors) mathematical knot theory ignores much of what makes the problem of knot-tying interesting. Some matters that come up in the ...
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0answers
230 views

damped harmonic oscillator driven by a stochastic momentum (not force)

Could you give references for solutions or solutions to the following problem: Given: damped harmonic oscillator driven by stochastic force of very short duration (= stochastic momentum). Find: ...
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1answer
95 views

Coordinates transformation and falling body trajectory

As it's well known, assuming the earth fixed and non rotating, the trajectory of a falling body with initial speed $v_0 = \{v_{0x},v_{0y},{v_{0z}}\}$ is contained in a plane. Assuming an observer in ...
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2answers
2k views

How to calculate active load on a swingset? [closed]

Related to this question from DIY StackExchange. Given a beam (a swingset) with three swings suspended from it. Each swing holds 450 lbs of stationary load for a total of 1,350 lbs of stationary ...
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3answers
249 views

Resource request: history of and interconnections between math and physics

Reading this article I became curious to learn more of (- study more thoroughly and *seriously*$^{\star}$-) the topic. Is / are there some good references - either papers, books and/or other ...
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2answers
1k views

Find average molecular speed in gas when temperature doubles?

I have the following formula. The task just says what happens to average speed of the molecules in a gas when the absolute temperature doubles? I don't know how to go about tasks like this. What am I ...
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2answers
862 views

What is the relationship between variance and energy

I was speaking with someone today who told me that variance, in the sense of probability theory, is equivalent mathematically to energy in physics. Can anyone elaborate on this relationship?
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1answer
52 views

A group of matrices satisfying a particular constraint(definition) of the group

Suppose that one wants to have a group of matrices that satisfy some constraints. (As for a similar example, Pauli matrices satisfy some particular constraints.) The constraint goes like following: (...
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1answer
120 views

Eigenstate and quantum mechanics position opperator

Quantum mechanics math question: Suppose that there is eigenstate $|q \rangle$ where $q$ is position observable . The question is, 1) What is eigenstate? How is this different from eigenvector? ...
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1answer
57 views

How to linearize $V=V_w+(V_0-V_w)e^{-kt}$

I have a physics homework and I was asked to transform $v=v_w+(v_0-v_w)e^{-kt}$ into a linear equation to be graphed. ($v_w$ is one variable that is constant and $k$ is constant.) $v$ is velocity ...
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4answers
898 views

Gram-Schmidt and zero vector

I have a problem concerning the orthogonalization of a coordinate system; this is necessary in the context of a normal mode analysis of molecular vibrations. I am working on H2O, giving me a 9-...
3
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1answer
127 views

Taylor expansion of $H = \sqrt{m^2 - \hbar^2 \nabla^2}$

$$ H = \sqrt{m^2 - \hbar^2 \nabla^2} $$ Suppose that there is a equation like this. How do you taylor-expand this equation? I am extremely confused.
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1answer
72 views

How $v=(-\sin\frac{\alpha}{2}\sin\frac{\beta}{2},\cos\frac{\alpha}{2}\sin\frac{\beta}{2},\sin\frac{\alpha}{2}\cos\frac{\beta}{2})$ is derived from…

In the book Quarternion and Rotation Sequences, I can't seem to work out how the final equation (colored in $\color{red}{red}$) is derived from the original equation (colored in $\color{blue}{blue}$). ...
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1answer
125 views

(Physics) Finding the angle(s) of launch which hit a target.

Given a coordinate and the launch speed, I need to determine which pair of angle, or angle allows a hit on said coordinate. I know, let's say, the common way, which is using the following equations: $...
3
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1answer
572 views

escape velocity using limits

I have the formula for a rocket's escape velocity from earth, $V$ being velocity, $v$ being initial velocity, and $r$ being the distance between the rocket and the center of the earth. $$V = \sqrt{\...
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1answer
2k views

What is the magnitude of the average frictional force on the block?

A $2.0 \space kg$ block, initially moving at $10.0 \space m/s$, slides $50.0 \space m$ across a sheet of ice before coming to rest. What is the magnitude of the average frictional force on the block? ...
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2answers
7k views

A trough is 3 feet long and 1 foot high. The trough is full of water…

A trough is 3 feet long and 1 foot high. The vertical cross-section of the trough parallel to an end is shaped like the graph of $x^2$ from -1 to 1 . The trough is full of water. Find the amount of ...
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1answer
40 views

Jumping from lower ground

I have a fixed initial velocity V(Vx,Vy,VZ) and a spot on higher ground E(Ex,Ey,Ez), my character must jump up there and he stands still at S(Sx,Sy,Sz). How Can I find the closest point to the ...
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2answers
5k views

Finding the maximum height a ball can be dropped from and still collide with a ball thrown below it

I don't necessarily need a specific answer, but I could use a hint, direction, or maybe some reading material. The question states: A rubber ball is shot straight up from the ground with speed $V(...
2
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0answers
71 views

Differential equations with different constants for different sub-domains

I remember that when I was studying differential equations, there was an example with solutions of the form $f(x) + C_1$ for $x>0$ and $f(x)+C_2$ for $x<0$ where $C_1$ and $C_2$ may be different ...
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1answer
133 views

Applications of mathematics to some kinds of sporting strategies

I am a rather newbie maths person. Haven't studied maths in a while and so not sure what things are called was hoping to get some information to push me in the right direction so I know what it is I ...
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1answer
732 views

Does apparent retrograde motion of planets begin and end at quadrature?

I've read it several places that the apparent retrograde motion of planets (during which they seem, as viewed from Earth, to move in the opposite sense of their normal "direct" orbital motion against ...
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3answers
138 views

Help with odd partial derivatives in velocity $\bar v^2 = \dot x ^2+\dot y^2$

I am doing a physics -course Tfy-0.2061. My teacher claims that this is velocity squared, $\bar v^2 = \dot x ^2+\dot y^2$. I cannot understand why it is not $\bar v^2 = (\dot x +\dot y)^2$. If ...
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3answers
219 views

Calculus and Physics Help!

If a particle's position is given by $x = 4-12t+3t^2$ (where $t$ is in seconds and $x$ is in meters): a) What is the velocity at $t = 1$ s? Ok, so I have an answer: $v = \frac{dx}{dt} = -12 + 6t$ ...
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2answers
438 views

What is the geometric, physical or other meaning of the tetration?

What is the geometric, physical or other meaning of the tetration or more high hyperoperations? Is it exists in general or it has only math concept?
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0answers
512 views

Equation of motion for a wobbling disc

While looking at a frisbee the other day, I suddenly had a question. Suppose (in free space) you set a disc-shaped object spinning, and then you impart a sudden force perpendicular to the spinning ...
2
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1answer
447 views

Finding the 'inhomogeneous' plane wave solutions of the wave equation via Fourier analysis

When one solves the wave equation $$ ( \partial_t^2 - v^2 \nabla^2) \mathbf{E}(\mathbf{x},t) = 0 $$ in $\mathbb{R}^3 \times \mathbb{R} $ using the Fourier transform method, the general solution is ...
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1answer
226 views

Function whose graph resembles the shape in this image

What is the function whose graph would resemble the shape found in the image below? I looked this up on Wikipedia, tried making my own, but I can't find an equation the Electromagnetic Spectrum. I ...
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1answer
187 views

What does it mean mathematically to set some of the integration constants in the general solution to a linear differential equation, equal to zero?

I'm trying to calculate the position of a particle in a quadrapole magnet depending on the entry position $x_0$ and the combined (constant) physical parameters $k$. Given an equation $$x(t) =\frac{(...
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1answer
1k views

Effects of gravity on diffusion [closed]

I'm just now learning the diffusion model and it seems that we aren't taking into account the acceleration due to gravity of the particles. Is this a shortcoming of the model or irrelevant? I don't ...
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2answers
179 views

Basic conceptual diffusion problem

Suppose that some particles which are suspended in a liquid medium would be pulled down at the constant velocity V by gravity in the absence of diffusion. Taking into account the diffusion, find the ...
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1answer
116 views

Is $\Delta^2V$ one of the nature's favourite patterns?

I was reading Sawyer's Prelude to Mathematics, he says that there's one suposed nature's favourite pattern which is: $$\Delta^2V$$ He also says that this pattern is found in a dozen areas: conection ...
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2answers
95 views

Thermodynamic relation

$$\left(\frac{dU}{dT}\right)_p= \left( \frac{\partial U}{\partial T} \right)_v + \left( \frac{\partial U}{\partial V}\right)_T \left( \frac{\partial V}{\partial T}\right)_p$$ Using maxwell relations ...
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2answers
305 views

How to find focal length of a convex lens?

I need help finding the focal length of a single convex lens. The radius of curvature is 200mm. left side is air and the glass has a index of 1.5. I search on google but there was only formulas for ...
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1answer
55 views

The signage of a displacement vector?

Well, on my homework I had these two questions, but got a bit confused about what they are asking, and whether my answer is right or not. What is the sign of the displacement if you are moving ...
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0answers
59 views

When can I treat vectors as regular variables when differentiating?

Given this Lagrangian where $\dot{\vec r} = \left(\dot x, \dot y, \dot z\right)^T$: $$ L = \frac m2 \left|\dot{\vec r}\right|^2 - q \left( \phi - \left\langle \dot{\vec r}, \vec A \right\rangle \right)...
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2answers
2k views

Find initial velocity given initial speed and rate of deaccelration?

Okay, So we are going over vectors in class, given Cartesian coordinates and convert them to polar, and vice-versa. So the question is that a skateboard rolls up a ramp shown in the image shown, at a ...
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1answer
582 views

Parametric curve of intersection - line integral with respect to arc length

This comes from Apostol's Calculus, Vol. II, Section 10.9 #14: A uniform wire has the shape of that portion of the curve of intersecion of the two surfaces $x^2+y^2=z^2$ and $y^2=x$ connecting the ...
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1answer
279 views

Physical meaning of spline interpolation

I remember that when I took my Numerical Analysis class, the professor said the spline interpolation take its name from a kind of wood sticks used to draw curved lines. Also Wikipedia say that the ...
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1answer
1k views

Scientific notation ratio conversion?

I wanted to know if I was thinking about this problem right and set it up correctly. It's been a while since I had to do math like this. The radius of the hydrogen atom is $0.529\times10^{−10}m$ and ...
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4answers
563 views

Trying to find angle at which projectile was fired.

So let's say I have a parabolic function that describes the displacement of some projectile without air resistance. Let's say it's $$y=-4.9x^2+V_0x.$$ I want to know at what angle the projectile ...