Recent content by bartekac

Okay, thanks. So I have also attempted to numerically solve the PDE, but I'm not sure about the boundary conditions that should be imposed with this problem statement. For the initial conditions, assuming that the geometry of the whole spring is compressed linearly, at ##t=0## we can say that...

Oh I see. And yes, in the end I would probably solve the PDE numerically. What I'm still confused about is applying the obtained solution to the problem. The way you derived the given equation, is ##u## the change in position between the initial location ##x## of a material element in the...

Thank you, this the bit I was missing. Completely forgot that the wave equation can be actually derived from the Hooke's law :) So the solution to the PDE would be obtained as Fourier series with Fourier coefficients computed from eigenfunction orthogonality, but I'm sort of confused about the...

Thanks for the answer. This all certainly makes sense, but what I am aiming for is incorporating this result into the dynamics of the spring itself. So assuming that the mass and the geometry of the spring is not to be neglected, how could we find the magnitude of the velocity of a certain point...

Yes, that would basically be my question and I'm seeking to find an analytical solution to the velocity field of the spring. Sorry if my initial statement was unclear.

Thank you for the response. Yes, I watched those videos back in the day. What I'm more confused about is how the increase of the kinetic energy of the whole spring is represented by the motion of a given point in the spring in the case when we consider the spring just extending by itself. I...

Hi, So I am currently working on a rather simple problem of a projectile being launched by a spring at a certain angle. Ignoring friction, from conservation of energy we know that the velocity of the launched projectile would be ##v = \sqrt{\frac{kx^2}{m}}## (with ##m## being the mass of the...

In general, what interests me here is how to approach the problem of calculating the compression of a fluid in the described situation. Can water still be considered non-compressible if the container was, for instance, moving with a linear velocity L\omega>\frac{1}{4}c?

Ok. I suppose the water density will increase as a result of centrifugal force causing the molecules to move closer to one another.

No, it is not. I was just concerned that I have actually no idea how to approach it.

Hi, I was recently thinking about a problem which I have no idea how to solve. A full water container with volume V is hanged on a rope with length L (mass of the rope is negligible). It then starts to revolute around the point where the rope is hooked (circular motion, circle with radius L)...

You are right, the shape influences the sound strongly, but I meant that the project will be for a long time in a prototype state. So basically - not everything at once, firstly I would do something with materials, because it should be a bit easier. Indeed it is, but I believe that the...

I wanted to omit the direct influence of shapes on the output sound for now - maybe I will try to do something about it in the future. I mean for the complexity reasons, the sound would be the same if you hit a wooden table with a silver sword and with a silver spoon. Applying only material...

voko, thanks for clarification. My first post was kind of introductory. I am currently working on a group project connected to game/simulation engines. We want to develop a system of soundmaps, that will be capable of real-time generation of sounds based on the quantities I gave in the bold...

Hi, I am not a native English Speaker, so some words might not be appropriately used below, but I will try my best to explain what I was thinking about. In general, I have never learned how acoustic waves emerge microscopically. The application of the theoretical knowledge I acquired was always...