Recent content by Redwaves

I get ##\vec{N} = (-cos(s), -sin(s) , 0)## And the limits I'm using are ##[0,2\pi]## for both ds and ##d\theta##, since I have a circle moving around a circle.

I think what you said make plenty of sense. It is exactly what I was looking for.

I think I understand. That begin to make sense. I had no idea about the equation you wrote and if ##\ddot{x}## = 0 then the mode don't occur. Thanks !

I understand that at t=0, all the blocks doesn't moves, but does it means that the block A shouldn't oscillate in that mode? so, this is the only mode that A is at rest. Furthermore, I don't know why a dot product between an eigenvector and the position vector give me the position for C. What's...

All right, I see. Can you confirm that what I said is not totally wrong?

I'm not sure to understand the ##\sin## If the amplitude of the beats frequencies is ##2A \cos(\omega_1 - \omega_2)t/2##. Does it means that ##x_a(t) = \cos(3+\sqrt{7})t / 2 (\cos (3-\sqrt{7})t/2)##. Thus, ##\omega_1 = 3## and ##\omega_? = \sqrt{7}## ? Using trig identity, I get ##(\cos(a) +...

I think I found something with what you said. In general if I have the eigenvectors and the eigenvalues and the system doesn't have any damping force, can I use ##x_a(t) = C_1 X_{1a}cos(\omega_1 t + \alpha_1) + C_2 X_{2a}cos(\omega_2 t + \alpha_2) + C_3 X_{3a}cos(\omega_3 t + \alpha_3)## What...

It is probably just me having hard time to understand the question. It says the amplitude is modulated by that function. However, I don't really know what that means. Once again I'm sorry.

I drew the system. Sorry If it wasn't clear.

Hi, First of all, I'm not sure at all how to start this question. I found the eigenvectors in a previous question, but I'm not sure if I need it to solve this one. I think I need to use the expression for the position and velocity. ##a_n = C_n cos (\omega_n t + \alpha_n)## ##v_n = -\omega_n...

Hi, I'm trying to find the area of this tube using ##\int \int ||\vec{N}|| ds d\theta##. However, I get 0 as result which is wrong. So at this point, I'm wondering if I made a mistake during the parametrization of the tube. This is how I parametrized the tube. ##S(s, \theta) = (cos(s), sin(s)...

Thanks! My issue was that I had put##R_{12}## on the same denominator right after the geometric series.

I get 1 - ##R_{12}^2##

I don't know if that is what you mean. ##T_{12} = 1 + R_{12}, T_{21} = 1 + R_{21} = 1 - R_{12}## However, I have ##1 - R_{12}^2##

It's a typo, I have ##R_{21}R_{23}## on my sheet. For some reason, I don't have any more preview while I type. It's the second term that shouldn't have the T's