I need to calculate the angle of a rigid body under constant angular velocity as a function of time. The RPM of the body is known, so the angular velocity is ω=2πf. Therefore θ=ωt=[RPM]2πt/60. How can I calculate the angle so that it 'resets' after a full rotation?
Homework Statement
Fermions and bosons combine through the reaction
F + F + ΔE = B
(so the creation of a single boson requires 2 fermions and some positive energy).
What is the ratio of fermions to bosons at T = 0?
Homework Equations
2[nF]/[nB] = K(T), where [nF] is the...
Yes, that was meant to be a sum, not a product.
How is the volume in 4D space? I had wanted to find the volume in 3D space, which should only requires a double integral. But I was not sure how to account for the density of the function changing in all three directions.
Homework Statement
How can I find the volume of a three dimensional gaussian exp\left [ \frac{-x^2}{\sigma_{x}} \frac{-y^2}{\sigma_{x}}\frac{-z^2}{\sigma_{z}} \right ] ? Since it is a gaussian, the volume should actually extend to infinity. It seems like there should be a simple double or...
I thought post # 3 and post 6 were equivalent through some trig identity.
I see why you applied the boundary conditions and set the coefficient on the cos(n\pix/L) term to zero. But if I want my wave to look and act like the progressive wave shown here...
You are correct. It is definitely not a real wave in the classical sense. I am familiar with the random walk, and I agree that that is what this is. But since the string will have an internal resistance to bending, that rigidity brings it back to equilibrium (so the resistance to bending is the...
Thank you, that makes sense. But why does Fn(x) only consist of sin terms, instead of both sin and cos terms?
What I originally had was y = Ʃ sin(nπx/L)*[An cos(\omegat) + Bn sin(\omegat] + cos(nπx/L)*[Cn cos(\omegat) + Dn sin(\omegat].
Is there a reason not to include the second term?
ps...
That's what I'm confused about. I know that I can express the motion of a vibrating string using sin and cos terms, but I don't know what BC's to apply if the ends of the string are free to move.
I want to express the shape of a string using sin and cos, but I am not sure what combination of...
What is [an] equation for a transverse wave with no boundary conditions, as a function of x and t? I want to model a fluctuation string where neither of the ends are bound.
I don't see how this is at all related to the 'goodness of fit'. It seems like it is really only dependent on the number of data points that were used.
I don't understand this at all. What are x_i, x_bar, and x referring to here? And shouldn't the uncertainty somehow depend on the y values for the data and the y values for the fit?
No, I hadn't considered conditional standard error- does that apply here, and if so how would I use it?
I said that the standard deviation of the fitted line (which I called the uncertainty on y_fit) was the square root of the variance of the residuals. The uncertainty for the fitted line...
I am fitting data to a parabolic equation using the least squares fit method. Each data point that goes into the fit is the average of 5 data points at that x value, so that each point has error bars that come from the standard deviation of those 5 y values.
I have a fitted equation, and I...