Recent content by Rome_Leader

Nevermind, I've solved it! For anyone interested in the solution, I just had to distribute the implication and then expanding was a lot quicker!

Homework Statement [ (p or r) & (not(p) or r) ] ---> r is a tautology. Prove this without using truth tables. Homework Equations See above. not(p) = !p = p' = the opposite value of p and ---> is an implication. The Attempt at a Solution I have made some prior simplification, and...

Homework Statement Integrate -π∫π H(t-π/2)*sin(2t)dt Homework Equations See above. The Attempt at a Solution I can rationalize the slightly simpler integral for the same limits of H(t)*sin(2t) as coming out to 0 due to the definition of the unit step function, but I'm wondering...

Ahh, I totally understand now! Thanks for that last bit, it helped give my mind a kick. Essentially it's the same as integrating from 0 to inf of just e^-2t given that H(t) is 1 starting from 0 and going on to infinity! Thanks!

Expanding, I get d^2y/dt^2 - (dy/dt)*b - (dy/dt)*a + ab. Your z substitution is a little confusing, but then I get (dy/dt-a)*(dy/dt-b) = 0 again?

Why does my calculator give 1/2, then? If I follow your logic, then I should plug in my limits of inf and -inf to e^(-2t), and this gives me 0 -0.

I follow, but that does not appear to express it in the form K1*e^(j*a*t) + K2*e^(j*b*t). I don't think it makes it any simpler either, at least not to my eyes.

Homework Statement I have a circuit with input source x(t), which contains also an inductor and a capacitor in series which I have found to be related to the output voltage y(t) (across the capacitor) like so: LC*d2y/dt2 + y(t) = x(t). I have also found its roots through the quadratic...

Homework Statement -∞∫∞ H(t)*e-2tdt Homework Equations See above. The Attempt at a Solution I know if I were just integrating H(t) by itself, I would get a ramp function. I also know e^-2t by itself will not converge for the given limits of +/- infinity. I just want to know what...

Update: Realized I could use Google to calculate such a sum, and got the answer! Now I have a new problem. The second part of that question asks for the same thing, but for the holes. It gives the effective hole mass as 5.10*10^-31. T = 298K this time. When I plug in the values, I get about...

Homework Statement Determine the total number of energy states in silicon from the edge of the conduction band to Ec + kT for T = 300K. Homework Equations N = \intg(E)dE The Attempt at a Solution I'm pretty sure I know how to do this one. The only problem is, when I get to the...

Homework Statement A beam of light of wavelength 600 nm passes through two slabs of material of identical thickness d= 1.40 micrometers, as shown in the figure. The slabs have different indices of refraction: n1= 1.41 and n2= 1.58. What is the phase difference between the two parts of the...

Homework Statement Calculate the electric field at the center of a square with side length .360 m. The charges, clockwise from top left on the corners, are Q1 = 4 x 10^-6, Q2 = 3 x 10^-6, Q3 = 1 X 10^-6 and Q4 = 5 x 10^-6 Coulombs. Homework Equations E = kq/r^2 where k = Coloumb's...

Assuming there are no other sources of loss (e.g. sound, temperature change, etc.) which is an idealized but very common situation when working out problems. If we are using your initial problem where only gravitational potential is concerned, then yes, what you gain in kinetic as you fall will...

Namely, what quantity involves mass and velocity, so we can use all your given data? What can we say about its value before and after the collision?