System Definition and 1000 Threads

Summary:: How can I get mathematics modeling for these tree systems? First of all, my mother tongue is not English, so my expression could be ambiguous. I want to get mathematics modeling for these three system above, like this form. First one is b -> (b1+b2), right? but I'm not sure...

$\tiny{311.2.2.6}$ Use the inverse to solve the system $\begin{array}{rrrrr} 7x_1&+3x_2&=-9\\ -2x_1&+x_2&=10 \end{array}$ the thing I could not get here without a calculator is $A^{-1}$

Hello, We know that most celestial objects in our solar system are in the equatorial plane of the sun. So too, does most of our spacecraft orbit in this plane as it explores our solar system. For a spacecraft already traveling away from the sun and towards the outer solar system, how hard...

Confused on how to find tension in rope (this would be the force acting on mass 2 that is causing work). Fnet wouldn't be 0 since the speed isn't constant and no acceleration is given. I'm sure I'm suppose to use the masses in an equation somehow, but I'm not sure how. It makes sense that the...

Hi! I am looking into a mechanical problem which reduces to the set of PDE's below. I would be very happy if you could help me with it. I have the following set of second order PDE's that I want to solve. I want to solve for the generic solutions of the functions u(x,y) and v(x,y). A, B and C...

hey there, I am confusing what is the right answer to this system of mass, I solved it a couple of time and I got different answers. can you help me with that? I need to find the expression of the acceleration of the 2 masses. thanks a lot,Adam.

It seems to me that Galileo and his successors benefitted from there being other bodies in the solar system other than the Earth and the Sun to prove that the Earth (and other bodies) orbited the Sun, and not the other way round. In an imagined solar system where the Earth has no moon, and...

Hey! 😊 I am looking at the following exercise but I think that I miss something. The statement is the following: We are given the following system of equations: \begin{align*}2a-2c+d-2e=&-2 \\ -2c-2d+2e=&\ \ \ \ \ 3 \\ d+2e=&-2\end{align*} 1) Is the system in echelon form? Justify. 2)...

Summary:: equation system of complex mechanism need to be done. Lagrange Formalism could be helpfull to do it but small errors could all destroy .. Hi everyone, I tried to find the equation system of the joined Mechanism (4 DoF). I think there is a mistake but I am not sure where is it . I...

Solve the system $x^5+y^5=33,\,x+y=3$.

It makes sense that a=2 would cause problems because then we wouldn't have a matrix of full rank and we'd be unable to determine a value for w. But the key also says that when b+4a^2-4a-7≠0. Why is that an issue? For example, if a=1, that just says implies that w=0. Through back-subsitution...

The first equation leads to x = ae^2t + be^t and the second equation leads to y=[1/(ln(sint+pi/2)+c)] this corresponds to the system a+b=1/c 2a+b=1 which has infinitely many solutions. what am I missing here?

Solve the following systemof equations: $\dfrac{xy}{x+y}=a$ $\dfrac{yz}{y+z}=b$ $\dfrac{zx}{z+x}=c$ where a,b,c are not zero

The Week magazine Oct 30, 2020 page 8 To be fair, it's not quite as simple-minded as that makes it sound, but it is still, to me, is a terrible idea. Another progressive education idea that is well-meaning but likely to be disastrous in practice. Here's an article with more detail...

Anyone know what the simplest possible self-contained numeral system for complex numbers would be, analogous to signed ternary for integers? My guess would be quarter-imaginary base (https://en.wikipedia.org/wiki/Quater-imaginary_base.)

In our class, we're using Wassermann's Thermal physics as textbook. I always try to solve all question which included in Text book. But sometime when I meet a problem that look like easy but actually hard, I'm so embarrassed. This problem do also. First, in the textbook grand potential for van...

$\tiny{27.1}$ 623 Find a general solution to the system of differential equations $\begin{array}{llrr}\displaystyle \textit{given} &y'_1=\ \ y_1+2y_2\\ &y'_2=3y_1+2y_2\\ \textit{solving } &A=\begin{pmatrix}1 &2\\3 &2\end{pmatrix}\\...

Is there any relation between dynamical system and Hilbert space(functional analysis)?

Build a tube to space. Use our atmosphere to push a ship up the tube.

Is it the lower the boiling point the better? As room pressure and temperature already can change the phase without working at vacuum? And the higher critical point means it is hard to reach super critical phase? But there is transcritical CO2 cycle, which the critical point is so low, and...

Hi, In some hydrostatic tables I can see many spring-shaped pipes that are traversed by oil. Spring is responsible for a kind of dampening that I ignore how to deal with. Do you have any idea of the physical principle behind it?

See attached. You can see how the car as a whole conserves angular momentum with earth. Car pushes back, Earth moves back and rotates, car accelerates forward. https://www.animations.physics.unsw.edu.au/jw/momentum.html However, the ground puts a friction force on the front non-driving wheel...

I tried approaching this by finding the tangential and normal electric fields. Is this the correct approach? I've attached a drawing of the surface provided. ##\oint_S E \cdot dl=0## ##E_{tan1}\Delta x-E_{tan2}\Delta x=0## We know that ##E_{tan1}=E_{tan2} Next, we can find the normal...

the acceleration of the center of mass is ##a_{cm} = F/(M+m)## I considered the forces on the block of mass m(when the system is at maximum extension) I got the equation $$kx - \frac {mF}{(M+m)} = ma_{cm}$$ and from that I got the value of the maximum extension $$x = \frac {2mF} {k(M+m)}$$ which...

We have been requested to run this on linux. I am able to read in the original base system and then I am able to enter the number. As soon as I enter the original number the system reads out "Enter the base of the output:" then does not allow the user to enter the second base. Instead it just...

Hello I am trying to teach myself some basic maths for astronomy from a book, namely trying to calculate the distance between two stars in a binary system. One thing i am confused with is what angular separation means and how it can be translated to true physical distance between them using...

Is China allways first at PISA test because they have the most people in the world so statistically they must produce the most number of talent children? Or they have the best education system?

After crossing out all the variables which I think equals 0 in the equation, I was left with: ∆PE + ∆U = Qin mg (0.2) + ∆U = 300 10*9.81*0.2 - 300 = - ∆U = -280J This was the answer I derived. However, the correct answer was supposed to be 123.3J. Please can someone explain to me how to get...

m1 = top left m2 = bottom left m3 = top right m4 = bottom right My questions: 1. Will all the object (m1, m2, m3,and m4) have same acceleration? 2. Should I assume initial extension of both spring is the same? (only based on the picture) 3. Will the extension of the spring change after the...

Find all real $x$ and $y$ that satisfy the system $x^3+y^3=7$ and $x^2+y^2+x+y+xy=4$.

Hi PF! I'm trying to solve three equations in Mathematica, but NSolve is taking FOREVER. Am I missing perhaps an easier way? The equations are below: NSolve[{1/2 r (r \[Theta] + (2 h + r Cos[\[Theta]]) Sin[\[Theta]]) == v, Cos[\[Alpha]] == -Sin[\[Theta] - \[Beta]], Tan[\[Theta]] == (-h...

Hello! I have some problem getting the correct answer for (b). My FBD: For part (a) my lagrangian is $$L=T-V\iff L=\frac{1}{2}m(b\dot{\theta})^2+mg(b-b\cos\theta)-\frac{1}{2}k\boldsymbol{x}^2,\ where\ \boldsymbol{x}=\sqrt{(1.25b-b)^2+(b\sin\theta)^2}-(1.25b-0.25b)$$ Hence my equation of...

In celestial coordinate system (right ascension/declination), how to check if an object with position RA and dec is within a given circular field of view of radius R (in arcminutes) and centred at (0,0)? R is small in this case so I assumed that I could compute the distance d of the object from...

To my understanding, to get the basis vectors for a given coordinate system (in this case being the elliptic cylindrical coordinate system), I need to do something like shown below, right? $$\hat{\mu}_x = \hat{\mu} \cdot \hat{x}$$ $$\hat{v}_z = \hat{v} \cdot \hat{z}$$ And do that for...

Hey guys, what is the difference equation of the signl seen in the figure ? my suggestion is: y(k) = 2u(k) + 2u(k-1) + 2u(k-2) - y(k-6)

How I would have guessed you were supposed to solve it: What you are supposed to do is just take the gradients of all the u:s and divide by the absolute value of the gradient? But what formula is that why is the way I did not the correct way to do it? Thanks in advance!

Greetings to all need forum members help regarding MCNP5 college assignment. The task is to calculate dose from a system comprising of a neutron source surrounded by natural uranium. the system is subcritical. The problem is how to calculate dose due to fissions in the uranium because dose from...

Dear mechanical expert I have to realize a linear displacement system for a Hall sensor that has to slide along the central axis of a narrow cylinder and with which high intensity magnetic field measurements (1-14 Tesla) have to be made. The field is produced by a commercial vertical magnet...

I am not sure if i get the question... At first i would say it is impossible to give a answer, we can not distinguish. But i think if we know the phases in this instant, we can give and answer, so my answer would be: "If we know, by some reason, what are the phase in this instant, we can give...

Find all integer solutions of the system of equations $x+y+z=3$ and $x^3+y^3+z^3=3$.

The first law of thermodynamics states that the change in the internal energy of a system equals the net heat transfer into the system minus the net work done by the system. In equation form, the first law of thermodynamics is ΔU = Q − W. in the mathematical expression of the first law of...

I cannot understand the solution at https://www.aapt.org/physicsteam/2015/upload/E3-2-5-solutions.pdf, because the solution is terse and skip steps (at least i think so). I figured out that the name of this transfer is "Hohmann-Transfer Orbit". A detailed walkthrough would be appreciated. If I...

I was just wondering what is wrong with the following logic; From the Gibbs-Duhem relation we get, ##\frac{\partial \mu}{\partial P}\Big\rvert_T = v## Now consider, ##\frac{\partial v}{\partial \mu}\Big\rvert_T = \frac{\partial }{\partial \mu}\Big (\frac{\partial \mu}{\partial P}\Big\rvert_T...

Find all the real numbers $a,\,b$ and $c$ that satisfy the following system of equations: $\begin{align*}a + b + c &= 1\\ \dfrac{a}{ 1 - a}+\dfrac{b}{1 - b} + \dfrac{c}{1 - c} &= 6ac + 6bc = (a + 1)(b + 1)\end{align*}$

and this is my solution for question (d), it may seems that $$R=(k)/(k-m\omega^2)R_0$$ so that $$\omega ≠ \omega_i =√(k/m)$$ but $$\omega_c <\sqrt{k/m}$$ is always true, ##\omega_i## corresponds to the limit case when ##F_max## is infinitely large Besides, I don't know other Physics prevents...

Can't visualize how the system moves, can anyone help me?

In some experiments of a complex physical mathematical system, we found some symmetry phenomenon, very similar as symmetry breaking phenomenon, say, as translatable sysmmetry etc. These symmetry (breaking) phenomenon occurs in most of the parts of the system or some parts of the system. Can you...

FBD Block 1 FBD Block 2 FBD Pulley B I'm mainly concerned with the coordinate system direction in this problem, but just to show my attempt, here are the equations I got from the system. ##-T_A + m_1g = m_1a_1## ##T_B - m_2g = m_2a_2## ##T_A - 2T_B = 0## Using the fact that the lengths...

I am trying to design/build a large self-filling drinking station, aka water bowl, for my goats and cow (see design attached). It's a takeoff of a dog's self-filling water bowl, i.e., uses gravity and vacuum to automatically refill the bowl as the water in the bowl is drank. The rain barrel is...