Tagged Questions
1
vote
1answer
75 views
Describe a sine wave of known frequency with only two points
This is my first post on math.stackexchange (sorry if meta people remove the Hello (sometimes we do that over on stackoverflow ;P)!
I have a system wherein I know that the output is a sine wave, with ...
2
votes
1answer
60 views
Trouble understanding a common vector calculus example
I have difficulty understanding the following vector calculus example. Text can be found here. It is the 5th Q&A -- starting with equation (31.1035).It concerns finding the vector potential of a ...
1
vote
1answer
23 views
Minimum Ejection Velocity
PROBLEM:
Calculate the minimum ejection velocity with which a shell must be fired to strike a target 1000ft high and directly overhead.
QUESTIONS:
I use integration to work back from 32ft/sec and ...
3
votes
2answers
34 views
Up and Down Motion (Two objects meeting in time?)
PROBLEM:
Suppose than an object is thrown upward with an initial velocity of 200ft/sec and that another one is thrown upward 5 seconds later with an initial velocity of 300ft/sec. When and where do ...
-1
votes
1answer
126 views
Electrostatic Potential Energy
How is the boxed step , physically as well as mathematically justified and correct ?
Source:Wiki http://en.wikipedia.org/wiki/Electric_potential_energy
As work done = $- \Delta U $. for Conservative ...
0
votes
1answer
37 views
Consider a pendulum that that has a length of $50$cm …
I am trying to do a simple pendulum problem but for some reason my answer is different from the book's answer and I don't know what I am doing incorrectly.
The question is:
Consider a simple ...
-2
votes
2answers
86 views
How to calculate work
What is the work done by the force of gravity on a particle of mass $m$ as it moves radially from $7500 ~\text{km}$ to $9400 ~\text{km}$ from the center of the earth?
0
votes
0answers
34 views
Taylor expansion of an integral in spherical co-ordinates
I've some difficulty deriving this equation from jackson electrodynamics (The equation after 1.30)
$\nabla^2 \Phi_a\left({\textbf{x}}\right)=-\frac{1}{\epsilon_0}\int_{0}^{R} ...
2
votes
1answer
59 views
Determine the Fourier Transform and Fourier Series of the function
$$
f(t)=\frac{\sin(at)}{t}
$$
Since the term is parameterized, it's easy to see that if I take the first derivative with respect to 'a', then the function becomes considerably easier. I do this to ...
4
votes
3answers
138 views
Physics notation justified
Sometimes in physics they do things like this one:
If $dq=f\left(x\right)\cdot dr$ then $\frac{dq}{dt}=f\left(x\right)\cdot \frac{dr}{dt}$
Which mathematically is a wrong deduction. Is there any ...
1
vote
2answers
96 views
Dirac delta function
1)Prove that the dirac delta function property:
$$ x\delta'(x)=-\delta(x)$$
2)and :
$$\int_{-\infty}^\infty \delta'(x)f(x)dx=-f'(0) \ $$
0
votes
3answers
336 views
Projectile Motion - Finding initial velocity
You need to send a bowling ball up exactly $205$ meters so someone at the top of the Washington Monument can take a picture of it "hanging" in space. The bowling ball will be shot from a mortar tube ...
2
votes
1answer
55 views
An integral for the Earth's insolation
Consider the function
$$
[-\pi/2,\pi/2] \ni \theta \mapsto s_\beta(\theta) = \int_0^{2\pi}
\sqrt{ 1 - \left(\cos \theta \sin \beta \cos \gamma
- \sin \theta \cos \beta \right)^2} \, d \gamma
$$
for ...
6
votes
0answers
101 views
Help computing an integral
I need to calculate the following integral:
$$
\int_0^1 \int_0^1 \frac{1-\cos(2 \pi k_1 x) \cos(2 \pi k_2 y)}{4 \sin(\pi k_1)^2 + 4 \sin( \pi k_2)^2} dk_1 dk_2
$$
I have tried to use some contour ...
2
votes
1answer
58 views
Center of Mass of “Combinations” of 1-Dimensional Objects.
Center of mass for one-dimensional objects is given by $\displaystyle\frac{\int x \, dm}{M}$ or $\displaystyle\frac{\int x \rho \, dx}{M}$, where $\rho$ is density. Now, the center of mass of a rod ...
1
vote
1answer
185 views
Finding the initial velocity using calculus
I throw a stone at 20 degree, when the stone falls to the ground, it reaches 100m further.
Using CALCULUS methods, find the initial velocity of the stone.
2
votes
1answer
81 views
Why are higher order differentials $dr^2$ and $ dr^3$ ignored here?
I'm doing a problem in physics, but it's the math part I'm curious about:
Charge density is defined by $\rho = \frac{dQ}{dV}$, then $Q = \int_{V}^{} \rho \text{d}V$
The problem is dealing with a ...
5
votes
3answers
337 views
Dirac Delta Function of a Function
I'm trying to show that
$$\delta\big(f(x)\big) = \sum_{i}\frac{\delta(x-a_{i})}{\left|{\frac{df}{dx}(a_{i})}\right|}$$
Where $a_{i}$ are the roots of the function $f(x)$. I've tried to proceed by ...
1
vote
1answer
109 views
Help with integral for electric potential
I need help evaluating the following integral
$$\frac{ \sqrt 2 \sigma}{2 \epsilon_0} \int_0^R \frac{r \,dr}{ \sqrt{(z- \frac{ rh}{R} ) ^2 + r^2} }$$
This integral pertains to the Electric potential ...
2
votes
2answers
613 views
solve for time given distance, initial velocity, and acceleration
I've been having trouble sorting this one out. I need to compute the time it will take for a vehicle traveling along a straight line to reach a particular point. I have the initial velocity ($v_i$), ...
1
vote
0answers
62 views
Where does the integral come from in this Spring formula describing displacement at a certain point?
I'm in the process of trying to combine some equations for a simulation.
One describes the position at a point along a hanging slinky using...
$$y(d) = (l_1 + {mg\over k})d - {mg\over 2k}d^2$$
...
0
votes
2answers
90 views
Show that the following cycle has a limit cycle
By direct calculation show that (using polar coordianted) that
$$
\dot x=x-y-x(x²+y²)
$$
$$
\dot y=x+y-y(x²+y²)
$$
Show that this has a limit cycle
I need help understanding how to test whether it ...
0
votes
0answers
121 views
sinusoidal word problem
in tidal waves the sea level drops first leaving the seabed exposed (normally 30 feet below sea level), then it rises a equal distance above sea level. waves hitting a city have a max height of 38.9 ...
3
votes
3answers
460 views
Cat Dog problem using integration
Consider this equation :
$$\sqrt{\left( \frac{dy\cdot u\,dt}{L}\right)^2+(dy)^2}=v\,dt,$$
where $t$ varies from $0$ to $T$ , and $y$ varies from $0$ to $L$.
Now how to proceed ?
This equation ...
2
votes
0answers
129 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 ...
0
votes
0answers
26 views
equality of Fourier integration of form with gradient
Non-locality comes from presence of infinite many terms in that
expansion. To see that, lets assume we are applying the non-polynomial
function $f(\vec{z})$ of $i\nabla$ on any function ...
3
votes
1answer
79 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.
-1
votes
0answers
52 views
Show the negative derivative [duplicate]
Possible Duplicate:
Show the negative derivative of a function.
A type of interaction between atoms in a molecule is called a Van der Waals interaction. This can be described by the ...
3
votes
1answer
116 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.
$$V = ...
0
votes
4answers
298 views
Show the negative derivative of a function.
A type of interaction between atoms in a molecule is called a Van der Waals interaction. This can be described by the potential energy function;
$$U= ...
2
votes
2answers
787 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 ...
2
votes
3answers
83 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:
$v = \frac{dx}{dt} = -12 + 6t$
...
1
vote
2answers
6k views
find average velocity and instantaneous velocity
The displacement (in meters) of an object moving in a straight line is given by:
$$f(t)= 1 + 2t + \frac{1}{4}t^2$$
where $t$ is measured in seconds.
Find the average velocity over the following ...
1
vote
1answer
77 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
$$x(t) ...
6
votes
2answers
71 views
Thermodynamic relation
$$\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$$
Using maxwell relations ...
3
votes
1answer
154 views
How come in classical mechanics we can get away with writing $a=v(dv/dx)$, treating $v$ as a function of $x$?
In classical mechanics we often use the relation $a=v(dv/dx)$ to help solve differential equations. I assume when we write $dv/dx$, we really mean $dV/dx$, where $V$ is a function defined so that ...
1
vote
3answers
766 views
Velocity Question & Acceleration
Below I have a question that I tried to solve on a exam. I am curious as to the actual way to approach the question. What I did was set the equation equal to $0$ and get $t = -3$ then I plugged in $3$ ...
3
votes
4answers
581 views
Hydrostatic pressure on a square
Vertically inserted into the water I have a rectangle 6 feet wide and 4 feet high that is submerged under the water with 2 feet of water above it.
Using a riemann sum how do I find the pressure? I ...
-3
votes
3answers
317 views
Hydrostatic pressure on a triangle
I am attempting to follow that horrendous site, Paul's calculus notes, but there are so many omissions or possible mistakes, I am not sure which.
I am following ...
-1
votes
3answers
1k views
Centroid of a region
$$y = x^3, x + y = 2, y = 0$$
I am suppose to find the centroid bounded by those curves. I have no idea how to do this, it isn't really explained well in my book and the places I have looked online ...
5
votes
2answers
420 views
Line Integral, Work in physics
Hi there all: I have a problem!
I need to find the work done on a particle that moves from $(0,0)$ to a point $(1,1)$ by a strait line $y=x$. The force acting upon the particle is $F = (y , 2x$).
...
2
votes
1answer
63 views
How do I figure out the speed of a jet of water in this example?
I should know how to do this but I don't. I'm not very familiar with vectors. Perhaps I will be after this.
So I have a stream of water falling out of a pipe. It obviously forms a parabola of the ...
4
votes
2answers
269 views
What's the relationship between Gauss' law and Newton-Leibniz formula?
Actually it's a puzzle I got in my Physics class.
Someone says Gauss' law actually is a specific example of the famous Newton-Leibniz formula, but I couldn't catch it.
So far I haven't learned about ...
0
votes
1answer
127 views
Why is $I$ = $\int_0^L R^2 \, dm$ considered a differential equation?
Earlier today in my physics course, we were talking about rotational inertia and how to calculate it for various shapes using calculus. Having not taken diff eq. yet, can anyone explain why this ...
0
votes
0answers
84 views
What curve best describes the cross-section of a river bed?
Assuming the water flows in one direction and at a constant rate and the material of the river bed is consistent, what curve would describe the cross-section of the river best (on the axis ...
0
votes
1answer
73 views
Does the centre of mass formula have other applications?
Taken literally, the centre of mass formulae for a 2d shape will give you the centre of a lamina that's described by two given functions between 2 limits. But I wondered if they might also represent ...
5
votes
3answers
222 views
The horizontal pivot line of $\sin^2 x$ here is exactly $\frac{3}{8}$. Why?
I noticed that the horizontal pivot line (or $y$-coordinate of the centroid) under the curve $y=\sin^2 x$ between $0$ and $\pi$ is exactly $\frac{3}{8}$. There may be no reason for me to find this ...
0
votes
1answer
74 views
What does the numerator represent in my centre of mass equation?
I've been trying to figure out how to find the centre of mass of some region under a curve. I figured out how to find the first pivot line parallel to the x-axis, but I can't figure out how to find ...
0
votes
1answer
277 views
Question about finding the centre of mass.
I'm working through Paul's Online Notes, and I'm on this page. I don't understand where the equations of moments come from. Can someone explain to me in the simplest terms how to derive these?
He ...
0
votes
1answer
283 views
Change of variables of PDE
I have a particle of mass $m$ that moves in 2-d in the potential $V(x,y)=\frac{1}{2}m\omega^2(6x^2-2xy+6y^2)$. I have to use the coordinates $u=\frac{x+y}{\sqrt 2}$ and $w=\frac{x-y}{\sqrt2}$ to show ...
