Recent content by RYANDTRAVERS

This is a question on fluorescence spectroscopy so physics/chemistry. What causes a large Stokes shift in the spectra? I know what causes the shift in wavelength, i.e., a relaxation of vibrational states before de-excitation to the ground state, but what actually causes a (very) large Stokes...

Well, yeah we defined it as \begin{equation} \Delta k \Delta x = 2\pi \end{equation} and then the rest can be derived from there.

Firstly, what does the 's' represent? Because, otherwise you can just equate the component of the weight along the inclined plane with the normal reaction force, which should give you: \begin{equation} \tan \theta = \mu \end{equation}

Homework Statement Consider a propagating wave packet with initial length L0. Use the bandwidth theorem to show that the minimum range of angular frequencies present in the wave packet is approximately: \begin{equation} \Delta \omega = \frac{v_{g}}{L_{0}} \end{equation} where vg is the group...

I agree with you that uf and ug are trivially 1; however, with the uxx there is the derivative operator with respect to x acting on ux to give uxx. I wasn't multiplying ux by ux.

Homework Statement Consider the function of two variables: u(x,y) = f(x-y) + g(x+(1/3)y) where f(s) and g(t) are each arbitrary functions of a single variable. Using the change of variables: s = x-y t = x-(1/3)y use the chain rule to determine the first and second derivatives of u with...

Don't worry, I was a little tired last night doing a 5 hour practice paper. I've got it now... silly me.

Homework Statement Consider a system composed of two species X and Y with fractional populations x and y, respectively, where x+y=1. The two species interact in such a way that the differential equation for x is: \begin{equation} \frac{dx}{dt}=xyA_{0}e^{-\alpha t} \end{equation} where $A_{0}$...

I’ve attached my attempt at the question. Just wanted to know what you think? I’ve got a definite integral that is a function of y, I(y), and have used the substitution t=tan(x/2).

How do you evaluate an integral such as: \begin{equation} \int_0^\frac{\pi}{2} \frac{1}{y+cosx} \, dx \end{equation} I was thinking whether to treat y as a constant and then integrate as such and be left with an arbitrary constant that is a function of y. This constant, f(y), should then...

I have a differential equation to solve below on the motion of an object oscillating in water with a restoring force equal to -Aρgx and a damping force equal to -kv^2. ma+kv^2+Aρgx=0 K, A, ρ and g are constants and I need to solve the equation for x. a (acceleration). v (velocity). x...