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First off, are you capturing all of the dynamics? In particular, are you modeling Jupiter's second dynamic form factor J2. This is fairly simple. It just means you need to take a tiny step beyond point mass gravitational models. Since Jupiter has a very large J2 (0.014733), you had better be modeling it. Jovian tidal dissipation, which transfers angular ...

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There's a really awesome trick for problems like this. This is going to be a long post but the method presented makes problems like this really easy. The idea is to turn the series branch $C_2$, $R_2$ into an effective parallel $R$ and $C$. See the diagram. The effective parallel values are denoted $C_{2,p}$ and $R_{2,p}$. Parallel capacitances just add, so ...

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Update: After simulating a little more, it seems that Drew Noel had the right hunch after all: by inserting a 100pF capacitor in parallel to the 110 Ohm and 11kOhm resistors, we can shift the resonance frequencies up from 11.25kHz to 12.11kHz, which gets us into the right ballpark. 150pF will give 12.71kHz for the upper frequency and 200pF will result in ...

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This is perhaps a comment to the @Floris answer. (I can move it there.) First about T1, It not only describes the decay of the Z-magnetization. But if you suddenly turn on a B field it also describes how long it takes the spins to become polarized in that direction. (Spins are not immediately polarized.) Concerning the decay of x-y magnetization. (I ...

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I don't consider myself an expert in MRI, but let me try (since nobody else has stepped up in the last hour...) You are right with your first assertion: the spin precesses about the B vector (this is why you get resonance in the first place). However, on average there is a net component of the magnetic moment aligned with the B field. This is what gives ...

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You can find the natural frequency of such a system theoretically, if you know the stiffness of the springs. Refer:this example on wolfram. How do you find the stiffness of the springs? Well... do experiments on simple pendulum, find the natural frequency from time period of oscillation, reverse calculate the stiffness of the spring as the mass of the test ...

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