# Search results

1. ### Basic crystal oscillator specifications question

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 ~16-25mW. So I've been looking to...
2. ### Oscilloscope trigger timing issue?

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 (1-3ns) between the...
3. ### Stern Gerlach expectation value

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...
4. ### Branch cut of the principle value log

1. Homework Statement Find the branch points of g(z) = log(z(z+1)/(z-1)) 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(z-1) the branch...
5. ### Stokes theorem application

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...
6. ### Hooke's law sanity check

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...
7. ### Protoboard circuit setup

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...
8. ### Neumann BVP steady state solution

1. Homework Statement U_t = u_{xx} - 4U u_x (0, t) = 0, u_x (\pi, t) = 1 u(x, 0) = 4cos(4x) Find a steady state solution to the boundary value problem. 2. Homework Equations n/a 3. The Attempt at a Solution Well i'm quite comfortable solving dirichlet/ mixed boundary...
9. ### Variation of parameters ODE what am i doing wrong?

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...
10. ### System of ODEs independent solutions

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} 2-r & 0 \\ 0 & 2-r...
11. ### Behaviour of implicit ODE solution as x approaches infinity

1. Homework Statement This is the solution to an IVP, and the question asks how the function behaves as x Approaches infinity...
12. ### Simple ODE uniqueness/domain question

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 non-linear ODE 3. The Attempt at a Solution I'm...
13. ### Non-standard basis matrix

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%20-3%20%5C%5C%200%20%26%201%5Cend%7Bpmatrix%7D%5Cend%7Bequation%7D.gif [Broken] Find the...
14. ### Maclaurin series power expansion

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...
15. ### Argon radioactive decay dating

1. Homework Statement The technique known as potassium-argon dating is used to date old lava flows. The potassium isotope 40K has a 1.28 billion year half-life 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...
16. ### Conducting spheres Gauss's law

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...
17. ### Particle travelling in magnetic field unit vectors

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...
18. ### Determinant problem

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...