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1. Inverse pendulum on a cart

This isn't directly answering your question but it may help at some point. Something I read once about balance is that it's not about making tiny corrections so you are always at the equilibrium position (i.e., in your case when theta = 0), it's about gently oscillating back and forth about the...
2. Greater kinetic friction

hmmm interesting question. I would say it would have something to do with a special material for the object that's moving, such that, as the object moves and the contact surface heats up due to friction, the surface undergoes some physical or chemical change so that its coefficient of friction...
3. Laser Modes/Free Spectral Range

Thanks, it makes a lot more sense now, and also, thinking about what the actual words mean in FSR, the range (ie a distance) that is free of spectral lines? (ie the distance betweeen spectral lines, or different modes since the modes correspond to slightly different wavelengths). I am aware...
4. Electomagnetic Induction

ok so you have a strip of magnetic material...its variably magnetized. This means that the magnetic field is different of different parts of the strip. Now what happens when you move the strip past a coil of wire? well we know the strip is magnetized so produces a magnetic field, so really...
5. Laser Modes/Free Spectral Range

thank you for the reply Claude. So the FSR is the longitudinal spacing of the modes only when the mirrors (or reflecting surfaces) are planar? otherwise we just just the term longitudinal spacing? About my second question, I was asking if the \Delta \lambda equation is correct for a laser...
6. Laser Modes/Free Spectral Range

Hi, As we know, lasers have longitudinal modes, the seperation between neighbouring modes (measured in frequency) is: \Delta \nu = \frac{c}{2L} and by using the fact that: \frac{\Delta \nu}{\nu} = \frac{\Delta \lambda}{\lambda} we obtain the seperation between neightbouring modes...