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The energy transfer is the work: force times distance. With a strike, the force is bigger and the distance (and time) is shorter. You could tune the two scenarios such that the work is the same. The big difference: when you cease to lean on the table, the table performs the same work back onto you (assuming reversible, elastic deformation), with zero net ...


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This is a tricky question. If the average force is really the same, what is going to change is impulse, the integral of force over time $$J = \int_0^{\tau} F(t) dt \simeq F_{av} \tau$$ When you push the surface you interact with it for a longer time ($\tau$), while when you smack it you interact with it for a shorter time. So if the average force $F_{av}$ ...


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Optical fiber is often used in sensor applications, including measurements of temperature and strain. This company describes many applications on this page. This article describes how optical fiber can be used to monitor vibrations.


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The physics in the 1st approximation are worked out here: https://en.wikipedia.org/wiki/String_vibration with the result that frequency depends on the length, tension, and mass density as: $ f = \frac{1}{2L}\sqrt{\frac{T}{\mu}} $ The 1st factor is why bass strings are long and treble are not (on a piano). The lower 3 strings on your guitar have a ...


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You can't; it isn't true as you've written it. You can trivially show this by taking some numbers (any numbers at all will do) for $T, \Delta T, v, \mu$ and plugging them in. What's going on is something else. $\Delta v/v$ can be written as a power series in $\Delta T/T$. What your professor put in the notes is the first-order term only. Thus, it is an ...


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This is a typical related rates calculation. The square root formula implies that $v^2=\frac{T}{\mu}$. Differentiating it we have $2v\,dv=\frac{dT}{\mu}$. Dividing the second formula by the first gives $2\,\frac{dv}{v}=\frac{dT}{T}$, which is equivalent to your increment formula. Of course, I replaced finite increments with differentials, so strictly ...


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All the example you have quoted can be regarded as oscillatory in that in some way the motion repeats itself be it with changing amplitude and/or with changing period. As an example would one use the term oscillatory for the motion of a pendulum? I think for most people the answer would be "Yes" even though both the period and the amplitude of the ...


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Damping implies a loss mechanism. In liquids, where molecules move freely in close proximity, this loss mechanism is a transfer of momentum from one molecule to another. In pure crystalline metals, the position of atoms in the lattice is fixed, and the forces between them are elastic. That is, if an atom is displaced, it will experience a force that puts it ...


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I'd like to point out the example of cast iron. It is renowned for its excellent vibration-damping properties. It is wrong to reach a blanket conclusion saying that metals are bad for vibration damping. The properties of any solid depends part on the material it is made up of and part on the micro-structure of the material. By micro-structure, I mean the ...


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Metals are not liquids (I am referring to metals which are in solid phase in standard conditions of pressure and temperature) and have no viscous mechanical dissipation on time scales associated with most mechanical vibrations. This implies that they can transmit transverse waves contrary to fluids. How efficiently they can do so is related to the details of ...



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