# Forced vibration with decreasing force amplitude

I'm working on a problem that has forced vibration. The force, every time it is applied, is less than the previous impact. For clarity, the problem is dealing with a mining skip that is emptying. The inside of the skip is separated in sections using ribs but the top blocks still exert a force on the lower blocks. The impact of the material hitting the bottom of the skip (a 50 degree angle) is causing the skip to vibrate. This impact happens at distinct intervals with the time between impacts remaining roughly constant. The impact force is decreasing due to the decreasing total mass of the material inside the skip. I was wondering if you could point me in the right direction. Most of the problems i have dealt with deal specifically with a periodic force that is constant each time it is applied. I thought about adding a dampening force to diminish the force each time it is applied but wouldn't that just act to dampen the free vibration component? For background i am an engineering student who is working on a project with an external company.

rude man
Homework Helper
Gold Member
I have no idea what a striker is, etc. etc. but you need to first determine the nature of each impact.

Is it a finite value of force (decreasing on each impact), EACH for a time interval T, or is it a series of decreasing impulses (Dirac delta functions), or ???

Then of course you need to determine the parameters defining your system. It had better be a second-order diff. eq. with constant coefficients. In other words, the equivalent of a spring, dashpot and mass.

Any other type of eq. & you have to use simulation software.

You're right, the damper does not solve your problem. You need to define the impacts by the forcing function in the diff. eq.

Once you have that you can solve the problem classically, or (as I would) using the Laplace transform. This is a transient problem, assuming the next set of impacts occurs much later.

PS - if the motion (vibrations) die down before the next impact arrives you have a much easier problem. But I imagine that's not the case or you wouldn't be asking in the first place, right?