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Standing Waves: finding the number of antinodes

A string with a fixed frequency vibrator at one end forms a standing wave with 4 antinodes when under tension T1. When the tension is slowly increased, the standing wave disappears until tension T2 is ...
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Functional determinant approximation

Let the Hamiltonian in one dimension be $H+z$, then I would like to evaluate $\det(H+z)$. I have thought that if I know the function $Z(t) = \sum_{n>0}\exp(-tE_{n})$ I can use $$\sum_{n} ...
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Acceleration by spherical particles (micron-scale) by an external force

I am looking for an expression for the velocity of a micron sized (1 - 10 micron diameter) sized particles under accelerating forces. I have aerosols in mind. This is what I have in mind The ...
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Calculating attracting magnets?

I have two identical bar magnets... Each bar magnet can lift an object with 10lb of force. When they attract each other, I believe that each magnet applies a force of 10lb to attract the other. That ...
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Mathematical Formulation of the laws of classical physics

By classical here I mean non-quantum mechanical, and everything that is developed afterwards such as color, etc. I am wondering if we can look at our Universe mathematically like this: Let ...
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Aerodynamic drag on a cannonball?

I'm trying to build a ballistics simulation where I shoot a cannonball. I want to allow for drag and am trying to work out the math to do so. I can work the drag out using $F = Cd\times S\times ...