This is a hard one, I still can't get it
Hey mang, you gonna help?
Yes yes. This is related to motion in a circle blah blah blah. Take the last poist where I made a mess up. Replace motion with cosines, that will be:
cos(wt) where w (omega) is angular acceleration. Integrating and differentiating should get you what you want.
Sorry, I've been on vacation.
Ok, I'm sorry for this long overdue response, but I am on vacation, away from the internet; I type this from an internet cafe.
Ok, I do not know how much about springs and calculus you know, so I will assume you know a little or nothing. So emperically we find the motion of one mass connected to a spring is proportional to a cosine function of the time. This is the same for vertical and horizontal systems as gravitation force plays no role in each (which can be shown analytically).
In fact we find for a vertical system (same as horizontal):
y = Acos(wt) where A is the amplitude of the motion and w (omega) is angular frequency, and not angular speed as I stated earlier. And
w= sqrt(k/m) where k is the spring constant and m is the mass.
The argument wt of the cosine function repeates every 2 pi radians or 90 degrees, therefore if T is the period (time to complete one complete cycle)
wT = 2pi radians or 90 degrees.
We also find the
F = -ks, where s is the extension from the equilibrium position, ie. a function of y. Therefore my'' = -ky which you can check solves if and only if w = sqrt(k/m)
We also make the assumption that the springs can be considered massless and all friction ignored.
In fact the general solution is
y = Acos(wt+h) where h is the phase shift, but that's unimportant for our needs.
Analytically we find:
A = sqrt(y0^2 + mv0^2/k) where y0and v0are the initial positions and velocities respectively.
y0 = Acos(h) and v0 = -wAsin(h) if we consider t0 to be t=0
Another way of representing y in terms of the initial conditions is:
y = y0cos(wt) + [v0sin(wt)]/w
Maybe this helps, I dont know, but is y(t) a function of the displacement relative to the top or the starting positions. I hope you can wrestle with that and get a solution, or someone will chip in and close the deal here, but I must leave now.
Yeah that helps, but I still can't come up with anything coherent...anyone else can?
Nobody else can help? I've been very patient, and I think this proves that this is not a homework or whatever
I'd appreciate even a try
Hi, can anyone look this over for me?
Anyone?!?!?! Please?!?!?!?!?!
One day, when my exams are over (long time from now), I will get back to you on this one. Dont hold your breath though.
Thanks bud, I appreciate it.
OK, soon, I'm thinking about the problem
Can you re-post the pic please.
Ya know what? I realised I couldn't do this problem myself, so I looked around, and this is the closest thing I cold find:
http://www.physicsforums.com/archive/index.php/t-203860.html
It's a bit over my head, as it involves coupled DE's, and quite a bit of Linear Algebra, but maybe you understand it. Sorry, I can be of no use to you
