Awesome. Thanks for the helpful responses -- I solved the differential equation and plugging in A*T instead of just "A" worked. I recall my professor mentioning that once during class.
I realize why my original guess wasn't a solution, too.
y''+9y=sin(3t)
I need to solve the above using the method of undetermined coefficients.
I have already found the solution to y''+9y=0 is c1(Cos3t)+c2(sin3t).
The problem is finding the particular solution. From class I am aware that the general form of the solution is...
I'm trying to run a simple regression for a data set (n=165). I've determined via a Chow Test that there exists a structural break somewhere; the same least squares estimate cannot be accurately used to represent the entire range of values the explanatory variable takes on. I've found two very...
Homework Statement
ABCD is a parallelogram with <BAD=60. Lines AM and BM bisect Angles BAD and ABC respectively. Perimeter of ABCD is 6. Find lengths of the sides of triangle ABM.
[PLAIN]http://img709.imageshack.us/img709/2440/stumped.jpg
The Attempt at a Solution
I'm stumped...
My question isn't related to natural sciences as most in this forum are, so I'm not sure this is the appropriate place to ask. I'm an undergrad junior (almost a senior) and am considering business school a few years down the road. I'm wondering, though, what kind of math should I have taken to...
One of the topics in my linear algebra course is kernel and range of a linear transformation. I have a firm understanding of what the kernel is: the set of vectors such that it maps all inputs to the zero vector. Range, however, remains nebulous to me. My textbook says that the range is "THe...
Wow, thanks for the helpful replies! :). ehild, it turns out that your derivation was one that was gone over in class during the one time I wasn't there :p (I had a medical appointment).
I found notes from a classmate and to sum it up the resulting formula is
\frac{-mr_{0}^2v_{0}^2}{r^2}...
Kepler's 2nd law says that the rate at which the radius vector sweeps area is constant. That is, the orbiting planet will adjust it's velocity accordingly to ensure that this is so. I'm not sure what the connection is between this and gravity is though.
I don't think the professor is suggesting that this is a plausible orbit. For what it's worth, this is a problem given to me in a class called History of Mathematics -- it's not a physics class.
Ugh, I was afraid of that. My professor is old fashioned and doesn't use textbooks for any of his classes. I've scoured the internet and my notes and haven't found mention of non-elliptical orbits.
Here's the exact wording of the problem:
"Suppose that in a universe where Kepler's second law holds, a planet revolves around the sun on the path with polar eq r= 1 + sin(theta). When theta = pi/2, the velocity vector and position vector are perpendicular to one another. Calculate the...