I need to create a 10 MHz square wave clock signal which gets terminated into a 50 ohm resistor for use by a waveform generator. The specifications for the waveform generator suggest a 12 to 14 dBm power level for the input clock. ie. a power level of ~1625mW.
So I've been looking to...
I'm using an arbitrary waveform generator that is generating a 1 MHz ramp waveform. I'm triggering on a marker sent out by the waveform generator which is tied to the same memory location as the start of the waveform. So although there is supposed to be a small latency (13ns) between the...
1. Homework Statement
An electron starts in a spin state \psi(t=0)\rangle = z \uparrow \rangle and evolves in a magnetic field B_0(\hat{x} + \hat{z}). The Hamiltonian of the system is \hat{H} = \alpha \vec{B}\cdot\vec{S}. Evaluate \langle \psi (t_{1/2})  S_x  \psi(t_{1/2}) \rangle...
1. Homework Statement
Find the branch points of g(z) = log(z(z+1)/(z1)) and defining a branch of g as the principle branch of the logarithm find the location of the branch cuts.
2. Homework Equations
3. The Attempt at a Solution
Since g(z) = log(z) + log(z+1)  log(z1) the branch...
1. Homework Statement
Let F(x, y, z) = \left ( e^{y^2} + y^{1+x^2} +cos(z), z, y \right)
Let s Be the portion of the paraboloid y^2+z^2=4(x+1) for 0 \leq x \leq 3
and the portion of the sphere x^2 + y^2 +z^2 = 4 for x \leq 0
Find \iint\limits_s curl(\vec{F}) d \vec{s}
2...
1. Homework Statement
4 springs with a mass on each end are connected in series as below:




m1




m2




m3




m4
All the masses are mass m, the length of each spring is 1, and the spring constant is k, find the extension of each spring.
2...
1. Homework Statement
Sorry if this is in the wrong forum, but it is for an introductory lab course.
I am trying to set up the simple circuit in part A of my drawing on a protoboard containing the components in part B of my drawing.
2. Homework Equations
n/a
3. The Attempt...
1. Homework Statement
\mathbb{x'}= \begin{bmatrix} 1 & 1 \\ 4 & 1 \end{bmatrix} \mathbf{x} \ + \ \begin{bmatrix} 2e^{t} \\ e^{t} \end{bmatrix}
Find the general solution.
2. Homework Equations
3. The Attempt at a Solution
Well i found the eigenvalues of the matrix That...
1. Homework Statement
so I'm trying to find the general solution of this problem:
\mathbf {x'} = \begin{bmatrix} 2 & 0\\0 & 2\end{bmatrix}\mathbf{x}
2. Homework Equations
det(A rI) = 0
3. The Attempt at a Solution
det(A  rI) = det \begin{bmatrix} 2r & 0 \\ 0 & 2r...
1. Homework Statement
Find the solution satisfying the given initial conditions for dy/dx = y/x, y(0) = 0 and explain according to the existence and uniqueness theorem.
2. Homework Equations
Existence/uniqueness theorem for nonlinear ODE
3. The Attempt at a Solution
I'm...
1. Homework Statement
Suppose the matrix standard matrix for a linear trnaformation T: R^2 >R^2 is[PLAIN]http://www.texify.com/img/%5CLARGE%5C%21%5Cbegin%7Bequation%7D%5Cbegin%7Bpmatrix%7D2%20%26%203%20%5C%5C%200%20%26%201%5Cend%7Bpmatrix%7D%5Cend%7Bequation%7D.gif [Broken]
Find the...
1. Homework Statement
Find the first three nonzero terms in the power series representation in powers of x (ie. the maclaurin series for: (the equation in the latex image below)
2. Homework Equations
fundamental theorem of calculus,
e^x = sum from n=0 to infinity of x^n/n!
3...
1. Homework Statement
The technique known as potassiumargon dating is used to date old lava flows. The potassium isotope 40K has a 1.28 billion year halflife and is naturally present as very low levels. 40K decays by beta emission into 40Ar. Argon is a gas, and there is no argon in...
1. Homework Statement
There are two conducting spheres, one hollow outer sphere which originally had +60nC of charge on it, and a smaller inner sphere enclosed by the hollow outer sphere which contains +20nC of charge.
2. Homework Equations
INT(E.DA) = Qenclosed/epsilon0
3. The...
1. Homework Statement
a particle with charge 2.00 C initially moves at v = 1.00 i^hat + 7.00 j^hat. If it encounters a magnetic field B = 60.00 k^hat T, find the force on the particle
2. Homework Equations
F = Q (v x B)
3. The Attempt at a Solution
I set up a matrix to find the...
1. Homework Statement
Suppose that the 6x6 matrix A obeys A^4 = 2A. Find all possible values of det A.
2. Homework Equations
Det(AB)=(detA)(DetB)
3. The Attempt at a Solution
Well my first guess is to show that A is either invertible or not invertible thus making Det A either...