Homework Statement
There is a capacitor (llenght ##L##) made of a conductor (cylinder of radius ##R_1##) and a cylindrical surface (radius ##R_2##). It is charged with a potential ##V_0##, then it is isolated.
(There is vacuum between ##R_1## and ##R_2##)
Now we insert a cylindrical...
I have a vector ##\textbf{v} \in \mathbb{R}^{3N}## and a function ##\textbf{Ψ} : \mathbb{R}^{3N} \longrightarrow \mathbb{R}^p##
such that ##\textbf{Ψ}(\textbf{v})=0##.
Why the set ##T=\{ \textbf{x} \in \mathbb{R}^{3N} \ | \ \textbf{Ψ}(\textbf{x})=0 \}## has dimension ##n=3N-p##?
Homework Statement
If I have the two curves
##\phi (t) = ( \cos t , \sin t ) ## with ## t \in [0, 2\pi]##
##\psi(s) = ( \sin 2s , \cos 2s ) ## with ## s \in [\frac{\pi}{4} , \frac{5 \pi}{4} ] ##
My textbook says that they are equivalent because ##\psi(s) = \phi \circ g^{-1}(s) ## where ##...
We know that energy is a function of space and velocity and it’s constant (in ideal case) though time.
So ## E(\vec{x}(t) , \vec{\dot{x}}(t)) = E_0##
where ##\vec{x} , \vec{\dot{x}} \in \mathbb{R}^3##.
So my function is ##E : \mathbb{R}^6 \rightarrow \mathbb{R}##.
Then there is my question...
In my textbook there is an explanation of a derivation of D'Alembert equation for pressure waves. (##\frac{\partial^2 y}{\partial x^2}=\frac{\rho}{\beta}\frac{\partial^2 y}{\partial t^2}##)
I put the picture (the only one I found on internet) but I'll call ##y_1 ,y_2## as ##\psi_1,\psi_2## and...
Hi everyone, do you know a trip/educational trip to do in summer for a 1st year undergraduate student in Physics (in Europe)?
I've heard about CERN summer students' school, but I think it' s alittoe bit too advanced for my knowledge of the subject.
Homework Statement
Reading chapter 4 of Morin's "Introduction to classical mechanics" I came across to the explanation of the damped harmonic motion.
The mass m is subject to a drag force proportional to its velocity, ##F_f = -bv ##.
He says that the total force of the mass is ##F= -b \dot{x}...