1
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1answer
59 views

Uniform Circular Motion with Banked Road and Car

In Uniform Circular Motion, if a car is rounding a curve at a certain speed, and the angle of the road allows the car to drive around at that speed, that speed is called the "design speed." If the ...
1
vote
1answer
42 views

Solving Simplified Hamilton's Equation

I have a question on a project that I am working on. I have included a large amount of the background information so that all relevant information is included, however the question is as follows (it ...
0
votes
0answers
29 views

Don't understand how this answer is arrived at; dynamic power

According to my notes the fomula for dynmaic energy is $\frac{1}{2}capacitive load \times voltage^2$ and formula for dynamic power is $\frac{1}{2}capaxitive load \times voltage^2 \times switching ...
1
vote
2answers
21 views

Getting the Amps from Watts, Amps and the voltage of a line

What amperage capacity should the supplied wired be rated for a refrigerated fixture which has a 208V power supply and the following loads? 4 Evaporator fan motor rated at 9W each 4 Evaporator fan ...
2
votes
0answers
62 views

Integral over orthogonal cylindrical harmonics

I am unsure how to solve an integral equation. As you know the orthogonality relation for cylindrical harmonics is: $$ \int_0^{2\pi}e^{in\phi'}e^{-im\phi'}d\phi'=2\pi\delta_{m,n}\ $$ The problem I ...
1
vote
2answers
31 views

Finding the magnitude of a vector product between two vectors?

Vector $\overrightarrow{A}$ has magnitude $11.0m$ and vector $\overrightarrow{B}$ has magnitude $16.0m$ . The scalar product $\overrightarrow{A}\bullet \overrightarrow{B}$ is $79.0m^2$. What is the ...
0
votes
3answers
63 views

Boxes on a slope [closed]

A box with friction slides down a slope and takes 2 times longer than a similar box with no friction takes to slide the same slope. What is $ \mu $ (the coefficient of friction)? I'm pretty lost. I ...
0
votes
1answer
27 views

Trying to understand free body diagram [closed]

Please consider the following image: Now I'm just trying to understand how exactly this thing is rotated...I'm looking at it exactly like on the image of the car...So the normal force is slightly ...
0
votes
1answer
51 views

Suppose that $\int _0^1 f(x)v(x)=0$ for every $v \in C^{\infty}([0,1])$ for which $v'(0)=v(1/2)=0$. Show that $f(x)=0$ for all $x\in [0,1]$.

Suppose that $\int _0^1 f(x)v(x)=0$ for every $v \in C^{\infty}([0,1])$ for which $v'(0)=v(1/2)=0$. Show that $f(x)=0$ for all $x\in [0,1]$.Suggestion: take u to be the suitable cut off version of ...
2
votes
0answers
39 views

Fock Subspaces and Weight Vectors

I've got an assignment due in a few hours, and I'm at a complete loss as to how to even start it, really. I haven't encountered any Dirac notation before, so I'm having a lot of trouble attempting the ...
0
votes
0answers
41 views

Equations of motion for a block

I am looking for a very simplified derivation of the equations of motion (rotational and translational) for a block with a body fixed frame. I need to compare the EOMs for a system when the center ...
1
vote
1answer
34 views

Compute the curl

Given that $\vec{\nabla}.{\vec{m}}=0$, and the vectors be in $\mathbb{R}^3$ I am trying to show that $$\vec{\nabla}\times \frac{r^2}{2}\vec{r}\times\vec{m}=(\vec{m}.\vec{r})\vec{r}-2r^2\vec{m}$$ I ...
0
votes
1answer
38 views

Periodicity on System of Equations

$$ y(t) = \begin{bmatrix} cos\sqrt\omega & -sin\sqrt3\omega & 0 & 0 \\ sin\sqrt3\omega & cos\sqrt3\omega & 0 & 0 \\ 0 & 0 & cos\omega & -sin\omega \\ 0 & 0 ...
3
votes
1answer
127 views

How do I calculate the following? (with answers)

Would anyone be able to help me calculate the following questions? I have the answers, I just want to understand the process. If you are able to give me any feedback, would you be able to write your ...
12
votes
1answer
198 views

Problem in Hamiltonian system

Not sure if this is too much physics to be here... Consider $$H:\mathbb{R}^{2N+1}\rightarrow\mathbb{R}$$ of class $C^2$, let $H(x,y,z)$ such that $x\in\mathbb{R}^N$, $y\in\mathbb{R}^N$ and ...
1
vote
1answer
50 views

What does this mean: Symmetry of the KDV generated by a vector field

What is a symmetry of the KDV $$\frac{\partial u}{\partial t}=6u\frac{\partial u}{\partial x}-\frac{\partial^3 u}{\partial x^3}$$ generated by $$V=A(t,x,u)\frac{\partial }{\partial ...
1
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1answer
71 views

Is the following differentiating under the integral sign correct?

Suppose $$\frac{\delta f[u]}{\delta u(x)}\equiv \frac{\partial f}{\partial u}-\frac{\partial }{\partial x}\frac{\partial f}{\partial u_x}+\left(\frac{\partial }{\partial x}\right)^2\frac{\partial ...
1
vote
1answer
300 views

How to solve a tensor differential equation?

Essentially, How does one solve the tensorial differential equation $$\frac{dx^a}{d\tau}=A^a{}_bx^b$$ where $x^a$ is a 4-vector and $A^a{}_b$ is a $(1,1)$ tensor. The original Problem How does ...
1
vote
1answer
50 views

Sketch the waves described by $y=(0.8\text{ meters})\sin[0.628(x-vt)]$

Ocean waves with a crest to crest distance of $10$ meters can be described by the wave function $$y=(0.8\text{ meters})\sin[0.628(x-vt)]$$ where $v=1.2 \text{ meters/s}$. a) Sketch $y$ at ...
2
votes
0answers
63 views

Laplacian of a function implies the function cannot have max or min.

If $\bigtriangledown^2f = 0 $ in some region in the space, then $f$ cannot have maximum or minimum on that region. My approach was to assume $f$ has a maximum and then use the second derivative test ...
0
votes
1answer
153 views

Find the parametric equation of the path of an object going at a speed x , with an orientation vector at time t and point p

$$ x = 1/2, v[2,−2], t = 3, P(1, 2)$$ x = speed, v = orientation, t = time, p is a point. I tried this : $$((2, -2) - (1,2)) \sqrt{1^2 + 4^2} $$ I got my <1,4> from $(2-1, 2-(-2))$ , which is my ...
3
votes
1answer
1k views

Frobenius Method to solve $x(1 - x)y'' - 3xy' - y = 0$

So, Im trying to self-learn method of frobenius, and I would like to ask if someone can explain to me how can we solve the following DE about $ x = 0$ using this method. $$ x(1 - x)y'' - 3xy' - y = 0 ...
1
vote
1answer
71 views

bundle isomorphism

Let $M$ be a manifold and let $U_{\alpha}$ and $U_{\beta}$ be coordinate charts with coordinates $x^{\alpha}$ and $x^{\beta}$, respectively. How to show that $f_{\alpha} : ...
1
vote
1answer
52 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 ...
3
votes
3answers
168 views

How to conclude this solution is periodic?

I've met the following problem in finishing my argument. The expression I ended with is $$\frac{\mathrm d}{\mathrm d\xi}U(\xi)=\pm\sqrt{C_1-\frac{U^4(\xi)}{2}},$$ with $U:\mathbb R\to\mathbb R$ and ...