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The answers currently posted are ignoring a few important details so I'm going to give my own. I may rehash some things already said. To make everything absolutely clear I write here a complete derivation of the forced damped oscillator with emphasis on the role of the $Q$ factor. Basic equations Consider the equation of motion of a forced, damped harmonic ...


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Sometimes when you're stuck on things, it's helpful to look at the mathematics of what's being asserted. For example, nowhere in Newton's three laws does "energy is conserved" appear. Energy conservation does appear, however, when you have a system that behaves like $m \ddot{x}=-\nabla U$, for some function $U$, where $x$ is a position vector as a function ...


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Derivation that applied work as defined above results, for a particle moving along a straight line, in a change in its kinetic energy (I hope it is not too complex to understand): In the case the resultant force $F$ is constant in both magnitude and direction, and parallel to the velocity of the particle, the particle is moving with constant acceleration a ...


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When two waves of a slightly different frequency encounter each other you will hear beats, which is nothing more than the two waves interfering with each other first constructively and then destructively, over and over as the waves go in and out of phase with each other. So now forget that there are two waves and concentrate on the sound made by the pair ...


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It is the time difference between successive maxima or successive minima. However, you cannot determine a beat period from less than 2 beats. I assume you are talking about music, because the standard scientific terminology defines the frequency of "beats per second" as Hertz.


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Doesn't the position function r(t) imply that a particle is traveling through the curve from A to B, separate from the influence of the force field since that is how parameterization is defined? Furthermore, isn't the force field that acts on such a particle that is moving on it's fixed path or curve C merely just changing the energy and speed at which ...


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Energy is a book keeping measure. AFAIK there is no such thing as "pure energy", merely energy as a measure of a property of a system with different degrees of attached entropy, the highest entropy state (generally) being heat which in turn is effectively kinetic energy. In other words, all energy tends to end up as kinetic energy.


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It is fully explained in this answer Angular momentum $ L = m*v*r$, since angular velocity is linear velocity divided by the radius, $ω = v/r \rightarrow v = \omega *r$ , then $L = \omega*[r*r*m]$ since $L = \omega*I \rightarrow I = m *r^2$ In the second sketch m=2, v = 3, r = 2 $\rightarrow L = 2*3*2 = 12 Kg*m^2/s$ Since angular velocity is v/r = ...


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The moment of inertia is linked with the kinetic energy. $$E_c=\sum_i \tfrac12 m_i v_i^2 = \sum_i \tfrac12 m_i (\omega r_i)^2 = \tfrac12 \omega^2 \sum_i m_i r_i^2$$ (wikipedia) It seems quite logical to me. Other reason is dimensional.


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First, there is no reason why a physical quantity must be linear in r. That only happens for some variables (perhaps the ones you are familar with). In the case of the moment of inertia, it is actually a multiplication of two linear variables in r, that is why it end result is quadratic in r. By definition: the moment of inertia is $I=L/\omega$, so ...


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The density operator combines pure quantum states into a mixed quantum state. The basic idea is to take a system composed of many pure states and to represent them as a single object, which evolves in time, as a complete system. In this example, the mixed state is represented as a Block sphere, and the $\vec{\sigma}$ is a pauli matrix. The Bloch sphere is ...



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