# system of equations

1. ### I Find the practical resonance frequencies in a system of linear differential equations

Hi all, I would like to know what is the equation upon which I can use to determine the practical resonance frequencies in a system of second order, linear differential equations. First some definitions: What I mean by practical resonance frequencies, is the frequencies that a second order...
2. ### A Need help solving Darboux equation

I'm working on a personal math project and I'm running into this system of differential equations. I have seen references which state the solutions are in terms of Hermite modular elliptic functions, but I do not know what those functions are. All of the references I can find on this equation...
3. ### Creating system of equations from word problem optimization

I have this word problem, and was wondering how I would go about creating a system of equations. Here is the question: Problem: You are a small forest landowner, and decide you want to sustainably harvest some of timber on your property. There are costs related to the infrastructure needed to...
4. M

### Finding values to make a linear system consistent

1. Homework Statement Given the following matrix: I need to determine the conditions for b1, b2, and b3 to make the system consistent. In addition, I need to check if the system is consistent when: a) b1 = 1, b2 = 1, b3 = 3 b) b1 = 1, b2 = 0., b3 = -1 c) b1 = 1, b2 = 2, b3 = 3 2. Homework...
5. ### I Solving System of Equations w/ Gauss-Jordan Elimination

I am fairly new here so I apologize for any mistakes in my post. My question concerning solving a system of equations using Gauss-Jordan Elimination is specifically about different ways to handle a possible constant. Say for instance you have three equations: X1+X2+X3 + 3 = 9 2X1+4X2+X3 =...
6. ### A How can I find the collision time of 2 ellipsoids that rotate

I have 2 ellipsoids: Ax^2/a^2+Ay^2/b^2+Az^2/c^2=1; (*a,b,c>0 constants*) Bx^2/a^2+By^2/b^2+Bz^2/c^2=1; Ellipsoid A rotates around axis [wax;way;waz] (unit vector) with an infinite speed; Ellipsoid B rotates around axis [wbx;wby;wbz] (unit vector) with an infinite speed; [Dx;Dy;Dz] is the vector...
7. ### Solving a system of nonlinear equations

This is actually not a homework problem, but a problem I'm encountering while working on a little project and I'm not sure if it's even solvable or if it makes sense what I'm doing 1. Homework Statement First, I have the equation p_{ij} = \frac{1}{2}\left( \tanh{(-\frac{\theta_i +...

1. The mb = 25 kg block is 2 m above the ledge. The pulley is a uniform disk with a radius of 10 cm and mass m = 4 kg. 2. (a) Find the speed of the 25 kg block just before it hits the ledge. (b) Find the angular speed of the pulley at that time. (c) Find the tensions in the strings. (d) Find...
9. ### B Verifying that all solutions to a system of eq. are found

I am given the following problem: Find all ordered pairs (a, b) such that $2a + b = 12$ and $ab = 3$. Given this system of equations, I simply use substitution, and then solve the quadratic $2a^2 - 12a + 3 = 0$. Solving this, I obtain two ordered pairs: ##\displaystyle (\frac{6 +...
10. ### B System of differential equations Basic question

So I ran into an case I have not seen before. Say we have a system of 3 equations such that W´=AW, where W=(x(t),y(t),z(t)) and A is a 3x3 matrix. The way I usually approach these is by finding the eigenvalues of A to then find the eigenvectors and thus find the ¨homogenous¨ solution. What...
11. ### I 4th order Runge-Kutta with system of coupled 2nd order ode motion equations

MX''=Fn(cosΦ−usinΦ) MZ''=Fn(sinΦ+ucosΦ)−Mg MΦ''=Fn(Bxx+uBz) I tried using Runge-Kutta methods to approximate motion equations in matlab but it turn out wrong. I also tired finding and researching forums and web for solution but to no avail. Fn,M,θ,u is constant fn/M = 0.866 it seems that i...
12. ### System of equations

1. Homework Statement this is actually one of the physics problems and I have boiled down the numerical to two equations. But I have trouble manipulating equations 2. Homework Equations Tsin(theta)=Fcos(theta)-mg and Tcos(theta)=(mv^2/Lcos(theta))-Fsin(theta) F and T are the two unknowns...
13. ### How do I solve these coupled Differential Equation?

1. Homework Statement dNa/dt = -Na/Ta where Na is the function and Ta is the constant dNb/dt = Na/Ta - Nb/Tb where Nb is the function and Tb is the constant 2. Homework Equations My Prof said Nb(t) has the form Nb(t) = Cexp(-t/Ta) + Dexp(-t/Tb) 3. The Attempt at a Solution I know the first...
14. ### Deriving the Compton Effect

1. Homework Statement I need to derive the equation related to the Compton Effect from the equations for momentum and energy conservation. 2. Homework Equations (1) Compton Effect: λ' -λ = h/me(1-cosθ) (2) Conservation of Momentum (x-direction): h/λ= (h/λ')cosθ+γumeucosΦ (3) Conservation of...