OK, I'm with you. So if I start with y = - Ax^2 instead of y = -x^2, I should end up with a solution of x = C_1 e^{\sqrt{2Ag} t} + C_2 e^{-\sqrt{2Ag} t}. Right? How would I find a value for A?
No worries for the slip. It was a good exercise for me. I was hoping that the solution would be fairly straightforward. Since this is getting much deeper than I am comfortable with, I am going to leave it at this point.
Thank you much for your help.
I get a solution to x'' - 2gx = 0
or (since g=32ft/sec^2)
x'' - 64x = 0
of x(t) = C1e8t + C2e-8t
Using the initial conditions, I get C1 = C2 = xo/2
and get as a final equation:
x(t) = xo/2(e8t + e-8t)
I've checked this several times, and It appears to me to be correct...
Taking the derivative with respect to time
2 v∂/v∂t = 4gx ∂x/∂t
v ∂2x/∂t2 = 2gxv
Can you please show me how you make this last step to the final second order diff. equation/
Thanks
Thanks so much Hootenanny,
I apologize for my ignorance.
I've been trying to teach myself differential equations, and it is VERY slow going. I learn best by applying what I am learning to real-world situations. I thought this problem would be a straight forward one to work on.
The...
Could you give me an idea of how to get started with this? I'm not familiar with Lagrangian mechanics.
It seems to me that if I could come up with an initial equation for acceleration as a function of time instead of as a function of position, it would just be a matter of integration to get...
I'm stuck on the solution of a problem. I'm looking for the general equation for the motion of a body with respect to time as follows:
A mass slides down a frictionless slope. The slope is not linear, but has the function y = -x^2 so that as the value of x increases, the acceleration...
I am new to quantum physics and mostly self taught. Please forgive me for what is probably a very naïve question.
Here's the way I understand it.
A beam of photons is directed into a Mach-Zehnder interferometer (two beam splitters, two regular mirrors, and two detectors). At the first...