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Re question 1: when you learn this stuff in school you usually simplify the system by modelling it as a simple harmonic oscillator so the amplitude of the system will be given by some equation like: $$A(t) = A_0 e^{i\omega_0 t}$$ where $\omega_0$ is the natural frequency of oscillation. Typically you study what happens if you apply a force that also ...

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A force can be applied with a certain frequency. Most accurately, for your example, energy will be transferred with a certain frequency. This means that, you can interpret this as a wave. The limit of amplitude of a vibrating object is related to the energy necessary to break or damage that object. The analogy of the swing may be misleading here. ...

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In signal processing, the Nyquist–Shannon sampling theorem says you need at least 2 samples of a frequency to be able to perfectly reconstruct it. So in your question, a sampling rate of $200\: \mathrm{MHz}$ means you can perfectly reconstruct frequencies in the range of $0 - 100\: \mathrm{MHz}$. So what happens when frequencies above $100\: \mathrm{MHz}$ ...

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According to this link http://www.flixxy.com/static-dripping-water-stroboscopic-illusion.htm It's not only real, but really cool. The amp is being played at the same frequency as the camera's shutter speed, so since the water is a solid stream as it exits the tube, each new drop falls into the same place the last one was when the camera takes another ...

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It's easy to see without doing any math, but just by looking at the picture. Let's consider first the case of low $k_{12}$. In this case, $m_1$ and $m_2$ basically don't notice $k_{12}$ because it is so weak that it is drowned out by the other springs. So the low $k_{12}$ case basically gives the same value as the $k_{12}=0$ case for all three frequencies ...

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The resistor only limits the flow of current not with $\partial I/\partial t$ example inductor it will opposes the flow of current when it will change with time means time i.e $T=\frac1f$ so frequency changes take in inductor that's why resistor is frequency independent inductor frequency dependent. $V=IR$, but Inductor $\mathrm{e.m.f}=-L ... 3 A monochromatic plane wave is simply: $$x(t) = A \sin\left(\omega t + \phi\right)$$ where$A$,$\phi$, and$\omega$are fixed, never-changing quantities. Because the properties of this wave never change, there is no way to use it to transmit information. Consider this: suppose you point a laser pointer from one building to another, so that you can see ... 0 The magnitude does not change with frequency, because the formula for an even wave is $$\Psi(x) = A\cdot e^{i(kx - \omega t)}$$ Where$A$is the amplitude and$\omega$is the frequency. So, if you change the frequency, the amplitude does not change. 1 It is absolutely correct that in vacuum all colors of light travel with same speed and this is why a white ray travels through the vacuum without suffering any dispersion... 1 I found a good paper that can help you. However, due to copyright issues I cannot put the spectra here. Try to get this article: "The Distribution of Energy in the Visible Spectrum of Daylight". A. H. TAYLOR and G. P. KERR. J. Opt. Soc. Am. 31 no. 1, pp. 3-8 (1941) . Also available here (pdf). 4 Do low frequencies carry farther than high frequencies? Yes. The reason has to do with what's stopping the sound. If it weren't for attenuation (absorption) sound would follow an inverse square law. Remember, sound is a pressure wave vibration of molecules. Whenever you give molecules a "push" you're going to lose some energy to heat. Because of this, ... -1 Wave always carry energy infinite distance. The energy of sound may dissipate along distance by many cause at the same rate in any frequency Low frequency wave not carry in "longer distance" than high frequency. But it may have less problem in propagate to things. Lower frequency wave tend to pass though bigger object with lesser absorb or reflect. So in ... -1 I think it has nothing to do with the frequency, but usual sounds consist of many fundamental frequencies and their harmonics, and usually you would have sounds built with such a formula like $$S(t)=\sum_{N=1}^\infty \frac{1}{N}\cos{N\omega t}.$$ So you see, lower frequencies would usually have higher amplitudes, and live longer. You can prove to yourself ... 0 The mass would scale in the other direction: as you increase the diameter of the plate, you would have to decrease the mass. This is due to the loss of stiffness as your plate gets larger. To give exact detail may require a little more information about the physical setup, but here are some basics. Frequency is related to$\sqrt{k/m}\$. Given the perceived ...

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