Homework Statement
A simple pendulum (mass M and length L) is suspended from a cart (mass m) that can oscillate on the end of a spring of force constant k. Write the Lagrangian in terms of the two generalized coordinates x and \phi, where x is the extension of the spring from its...
I guess this is maybe more algebra than calculus, but it stems from a calculus problem, so I'll stick it here.
The problem is:
In the case of the simple harmonic oscillator the solution [to the EOM] may be written at least 3 ways
x(t) = Acos(wt) + Bsin(wt)
= Ccos(wt + del)...
Homework Statement
Slope-matched parabolic sections. Consider the function of period 4 defined over the interval [-2,2] by the equations:
f(t) = 2*t-t^2 for 0<t<2 and f(t) = 2*t+t^2 for -2<t<0
It has a Fourier expansion \sum_{m=0}^\infty \frac{32}{\pi^3*(2m+1)^3} sin((2m+1)...
In present day, Co is 15.2, which is what it was when the shroud was first made. This value decreases by half every 5730 years, so the formula to use would be C_{o} (.5)^\frac{t}{T} = C where Co is the initial amount of carbon, C is the amount of carbon after t years, and T is the half life.
2. I could attempt, but not many people get to do that. Usually very good pilots go on to become astronauts, and I don't want to be a pilot.
3. I definitely have choices. :) I actually don't even know if I could go to the Naval Observatory, maybe for a shore tour for a more senior officer...
Success! y = \sqrt{-x^2 + x + 1}
Thank you SO much! No one in my class has been able to get that, we've been frantically IMing back and forth all night.
Yeah, but I can't separate it! Or rather, I can separate it, but I get completely unworkable results. It tends to fall apart when I get to
-ln(u^2 + 1)/2 = ln(y) + C
Never expected to be pleading for help so soon, and especially not on a differential equation, which I usually am good at. But for whatever reason, I cannot solve this problem:
y*d(y,x,2) + (d(y,x))^2 + 1 = 0
Any help would be greatly appreciated!
ETA: I know I'm supposed to substitute...