Thank you for that link, I haven't had a chance to go through it in detail (it's been a hectic week), but it does look promising, I just need to figure it all out!
I'm trying to solve this problem via Lagrangian mechanics, but I'm having trouble correctly formulating the problem, I'm hoping one of you kindly people can show me where I'm going wrong.
A pendulum bob of mass m hangs in the equilibrium position from a light, inextensible string of length l...
A cylindrical space station of radius r with thin walls and mass M rotates at angular velocity ω such that the apparent gravity on the inner surface of the cylinder is equal to g.
1) Radial spokes of negligible mass connect the cylinder to the centre of motion. An astronaut of mass m climbs a...
Thank you very very much!
So the phi terms have to be zero because the coefficients are non-zero and sum to root3 times B+ω+, meaning that the sin terms have to both be zero for all values of B and ω. Is that right?
And should the final answer be left in terms of B and not x0 or something...
I think I see why. X1,2 represent the changing position of the two masses over time as a combination of the normal modes, and the magnitude of each mode relative to the other is determined by the A and B values.
But how do you find the B values and phase constant? Everything I've read or...
Thank you for your replies!
The goal is to find A and B, right?
How do you use the phase factor to solve the equations? I mean, what calculation do you do with it to make this work?
I don't quite get a when I retry e, I get 2mx..1 = -k(2x1-x2
But I've pretty much given up on that...
I've had lectures on Lagrangian mechanics, but even after the lectures I still don't have a clue how it works, so that probably wouldn't be very fruitful. I also don't have a copy of Taylor sadly.
The derivation you linked uses the same sort of method as the one I followed to get to this point...
I've been trying other things, but it still doesn't work.
I know that the amplitude of the reflected and incident waves added will equal the amplitude of the transmitted wave, and that dy/dx at 0 will also be equal for the sum of the incident and reflected waves, and the transmitted wave...
I can't make this question work, so I'm hoping that someone here will be able to help guide me towards a solution.
I began with F=ma, and wrote down the equations of motion for each of the masses.
a) 2mx..1 = -kx1 -k(x1 -x2)
and
b) mx..2 = -kx2 +k(x1 -x2)Then I added b to a, and subtracted...
Thank you for your reply!
I think I get the idea there, but unfortunately I'm not having much success doing it.
As I understand it, solving the wave equation means solving ∂2y/∂x∂t = 0
(I don't understand why you do that though. Am I wrong in thinking that's the way you solve the wave...
This is the problem I'm working on: http://i.imgur.com/PBMFG.png
I'm very behind with normal modes and waves, and I need to figure out how to do this sort of question in time for my exams, so I'm hoping that you guys will be able to help me see how this can be answered.
I've answered the...