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...
The original problem for anyone that can read Chinese:
https://zerojudge.tw/ShowProblem?problemid=b221
The problem defines a convex polygon with multiple points located in the first quadrant and the required task is to find a linear function y = ax that can spilt the polygon into two parts each...
Hey all,
I don't understand what makes a differential equation (DE) linear.
I found this: "x y' = 1 is nonlinear because y' is not multiplied by a constant"
but then also this: "x' + (t^2)x = 0 is linear in x".
t^2 also isn't a constant.
So why is this equation linear?
1. Homework Statement
Find the distance from point P (1,7,3) to the line
(x,y,z) = (2,1,4) + s(1,3,4),
s is a free variable
2. Homework Equations
projnQP = ( QP⋅n/(lengthQP)(lengthn) )(n)
3. The Attempt at a Solution
I'm not quite sure about how to find the normal (n) here, but if I make...
1. Homework Statement
Find the cosine of the angle determined by the intersecting lines
m1: (x,y,z) = (2,1,4)+s(1,3,4)
m2: (x,y,z) = (2,1,4)+t(2,3,2)
s and t are free variables
2. Homework Equations
a⋅b = length(a)length(b) cosθ
3. The Attempt at a Solution
I just did this equation...
1. Homework Statement
Let A and B be nxn matrices with Eigen values λ and μ, respectively.
a) Give an example to show that λ+μ doesn't have to be an Eigen value of A+B
b) Give an example to show that λμ doesn't have to be an Eigen value of AB
2. Homework Equations
det(λI  A)=0
3. The...
Hello!
I have a question that maybe has to do more with Mathematics, but if you do experimental physics you find it quite often.
Let's assume that we want to measure two quantities x and y that we know that they relate to each other linearly. So we have a set of data points xi and yi...
Hi, I have in a previous thread discussed the case where:
\begin{equation}
TT' = T'T
\end{equation}
and someone, said that this was a case of nonlinear operators. Evidently, they commute, so their commutator is zero and therefore they can be measured at the same time. What makes them however...
Hi, I read that linear combinations of a state, Psi, can be as:
\begin{equation}
\Psi = \alpha \psi + \beta \psi
\end{equation}
where ##\alpha## and ##\beta## are arbitrary constants.
Can however this be a valid linear combination?
\begin{equation}
\Psi = \alpha \psi \times \beta \psi...
 This is the situation provided where it has to be demonstrated that linear momentum is not conserved or unrealistic. My assumptions are: there's no friction due to how Godzilla is moving, the sand is acting as a lubricant. Velocity is constant. This is an elastic collision. I also guess that...
I know there can be an infinite number of solutions when the objective function with 2 variables has an equal slope as a constraint's slope (assuming the constraint is affecting the feasible region and not a redundant constraint).
How can you know there are multiple optimal solutions for...
1. Problem
Recall that we defined linear equations as those whose solutions can be superposed to find more solutions. Which of the following differential/integral equations are linear equations for the function u(x,t)? Below, a and b are constants, c is the speed of light, and f(x,t) is an...
Hey. I am working with OLS regression. First I run 2 regression operations with each having just one independent variable. Then I run another regression using both the independent variables from the first two regressions. If the explanatory "power" (R^2) in the third regression was to be the sum...
1. Homework Statement
I did an experiment on how stretching a rubber band, affects the range or distance of a projectile shot.
Variable list:
Independent Variable
Amount of stretching
Dependent Variable
Range or distance
I created my catapults on my own and used two different rubbers...
Hey.
I am doing a project where I am studying a set of companies over a 7year period. I am doing a multiple linear regression analysis either with fixed or random effects (so, it's a panel study). What I am wondering is if the general assumptions/requirements apply when using the fixed/random...
1. Homework Statement
Find the general solution of y^{(5)}y(1)=x
3. The Attempt at a Solution
I found the complementary function by substitution of the solution form y=e^{kx} giving k=0,1,1,i,i, so y_{cf}=a_0+a_1e^x+a_2e^{x}+a_3e^{ix}+a_4e^{ix}
Now for the particular integral, the...
1. Homework Statement
Please bear with the length of this post, I'm taking it one step at a time starting with i)
Let A: I → gl(n, R) be a smooth function where I ⊂ R is an interval and gl(n, R) denotes the vector space of all n × n matrices.
(i) If F : I → gl(n, R) satisfies the matrix ODE...
1. Homework Statement
This is the second problem from our test preparation cycle and i partially solved and understood it.
The circuit in the picture is in the state of switch being open (STATE 1: SWITCH OPEN). Calculate ##E1## so that the change in the electrical energy of the capacitor is...
1. Homework Statement
This is one of the problem i had had some help in solving but some things remain unclear to me and i will highlight them by posting the exact question in the brackets next to the line of solution so that you can see what bothers me. Hopefully you can help me better...
1. Homework Statement
Show that elementary row operations don't affect solutions sets in linear systems
2. Homework Equations

3. The Attempt at a Solution
It's pretty easy to come up with a random linear system and perform ERO on them and showing that solutions are not affected, but is...
1. Homework Statement
In the circuit above ##E_1=E_2=E_3##, ##Ig_1=Ig_2=Ig_3## and ##R_1=R_2=R_3=R_4##. In the case when the switched is closed the power of the ideal generator ##E_2## equals ##P_{E_2}=30W##. Then the switch opens. Calculate the ##ΔP_{E_1}##.
2. Homework Equations
3. The...
I am given the equations of Lorenz with respect to deterministic nonperiodic flow:
\frac{dX}{dt} = Pr(YX), X(0)=X_{0}
\frac{dY}{dt} = XZ + rX  Y, Y(0) = Y_{0}
\frac{dZ}{dt} = XYbZ, Z(0) = Z_{0}
where Pr is the Prandtl number, r = Ra/Rac is the ratio of the Rayleigh number to its...
1. Homework Statement
How exactly they combined equation1 and equation2 and got that system? I don't get that part.
2. Homework Equations
A*(dy/dt)= k*y eq1
A*(dz/dt)=kykz eq2
3. The Attempt at a Solution
I tried substituting the 1st ky in the 2nd equation and then differentiating but...
1. Homework Statement
[pardon my crude drawing]
Say I have a ball that hits the a rod at rest pivoted around hinge A. The ball in the diagram is the solid black, and the rod is the thin line in the diagram and is rotating around the squareshaped hinge at the bottom. I am not an artist but...
1. Homework Statement
Linear Programming Case Study  Case Problem ( Page # 109 Decision making methods) “The Possibility” Restaurant?
In the case problem, Angela and Zooey wanted to develop a linear programming model to help determine the number of beef and fish meals they should prepare each...
1. Homework Statement
Find the equation of all planes containing the points P(2, 1, 1) and Q(1, 0, 0)
2. Homework Equations
3. The Attempt at a Solution
I use PQ to get a vector, (1, 1, 1). I some how need to use another vector so I can use the cross product to find the planes.
So i...
Okay, so I'm down to the last equation.
12/11 x 10 + 54/11 I get 66/99. Is this right? If so how do I put it into the graph.
12/11 x 10 = 120/110 + 54/11 = 66/99 (I think I've went wrong somewhere)
In linear accelerators that use a disk loaded structure (traveling wave), how would you calculate the iris(disk hole) radius, cavity radius, and disk thickness according to the wavelength