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    Series solution to a PDE

    Nevermind, that way should work. However, you seem to have miscalculated your h_n. One trick you can do (if you have time and the ability to do so) is to plot the series (to a reasonable amount of terms) and see if it matches the function you're trying to represent. Anyway, you're actually on...
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    Series solution to a PDE

    Why are you saying that x sin(t)=\sum_{n=1}^{∞}h_n(t)sin(nx) ? What if you chose a solution that was periodic in time with an unknown function of x, rather than the other way around?
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    When everything looks equally interesting

    I'd say delve deeper into each subject and talk to people who have degrees in the things youre interested in. Know that you will your coursework will not necessarily reflect your work once you have a degree.
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    DC motor mounted on a glider which slides linearly on a frictionless surface

    If I'm understanding your description correctly, yes you should. What you're effectively doing is having it shift the center of mass of the system. It will "try to correct itself" by exhibiting reaction forces on the rest of the system to keep the center of mass constant. Based on what...
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    Meaning of (A dot nabla)B

    What you're talking about is called the Advective or Convective operator and describes the change in a property due to flow of continuous media (in Fluid Mechanics anyway). Char limit is correct. Don't worry about whether it makes sense or not the way it's written because it is essentially...
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    Engineering Women in Engineering and Computer Science

    In my experience, women get preference to men as far as getting jobs in Engineering. All the girls in my classes I know, even the ones who have sub-par GPA's got snatched up immediately when it came time to look for internships.
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    Is knowing a computer language vital for someone pursuing Theoretical Physics?

    I know a lot of physics researchers work with R and MATLAB, but I only know that because a few friends of mine work in Physics and Astronomy labs. I can't speak from personal experience or anything as to Theoretical Physics, but it never hurts to learn a good computer language. I personally...
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    Thermal Resistances

    Thermal resistances simplify problems wherein there is no heat generation within the system. If there is a KNOWN heat generation entering the system, like if you have a sliding block which is experiencing friction on one face, you can find the the heat flux on that side. But if it's like a wire...
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    Transition from pressurised envoronment to vaccum environment

    Where are you getting this notion that that sort of technology exists or even is anywhere near usable?
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    Relationship between differential and the operator

    Your professor is wrong. dx * d/dx = d. In words, the change [of something] per change in x times the change in x is the change [in the thing].
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    Mouse onto the edge of phonograph turntable

    There is a centripetal acceleration associated with rotation at constant angular velocity, a_c = \omega^2 r . So if my suspicions are correct, you can interpret that as a force that must be overcome, F_c = m \omega^2 r
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    Angular acceleration without rotation?

    This is also a kinematics problem, not an introductory physics problem, and involves using relative velocities.
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    Angular acceleration without rotation?

    It's not fixed at collar C, it's sliding through it. It if were fixed, there would be 0 degrees of freedom, and OB could not be rotating.
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    Basic circuit question (True/False)

    1 should be correct. As for 2, when the switch is closed, the total resistance goes from (1.5)R to (1.333)R. Less resistance means increasing the total current pulled from the voltage source. In fact, you can find the total open-switch current, iopen=V/(1.5R), and the closed-switch current...
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    Basic circuit question (True/False)

    I thought you said the bulbs were identical?
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    Buoyancy problem in two liquids

    To my knowledge, that is the most logical method. I think perhaps if you could want more than that, you don't quite understand fluid statics and should read your textbook.
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    Buoyancy problem in two liquids

    To find the pressure on the bottom of the block: p_{\text{bottom}}=\rho _A g h_A+\rho _Bg h_B where h_A is the height of liquid A and h_B is the height of liquid B Then, as a force, F_{\text{bottom}}=p_{\text{bottom}} * A_{\text{bottom}} But this should be self-explanatory.
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    Basic circuit question (True/False)

    Brightness is proportional to power output, and in this case we care about the amount of current passing through. The current is at a maximum through bulb 1, and this divides into 2*1/2 before the switch is closed and 3*1/3 after the switch is closed. So the current through bulb 1 is always the...
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    Buoyancy problem in two liquids

    Think of it this way: at every point in any stationary liquid, there is hydrostatic pressure which is a function of the density of the fluid and the depth into the liquid. There is a force exerted on the block due to fluid "A", but it is inward and balances out because it is acting all along the...
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    1D oscillator solving for Amplitude

    I don't think you have to worry about the angular displacement term \delta since it's just one harmonic oscillator without any reference displacement.
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    Engineering material data

    Curious, why do you want properties of structural steel up to above the melting point of most steels, and well above the solidus transition I'm not familiar with phase transition in structural steel particularly, but I do know that you have to keep phase transitions in mind because they can...
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    Heat conduction in a beam with variable x-section

    I tried finding a solution for an average cross-sectional area but there was a rather large error, especially when using a largely variable cross-sectional area, like one proportional to x^4 (which was in the problem that made me wonder about it). Also, that formula for resistance is based...
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    Engineering material data

    Have you tried ?
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    Heat conduction in a beam with variable x-section

    Thanks for the guidance! I was able to derive this: \rho \text{Cp} \frac{\partial T}{\partial t}=\frac{1}{A(x)}\frac{\partial }{\partial x}\left(k A(x)\frac{\partial T}{\partial x}\right)+\dot{q}(x) where A(x) is the cross-sectional area of the beam as a function of the lateral...
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    MSME: How high should/could I aim?

    Hello all, I'm in my junior year of undergrad at Louisiana State University (LSU) and I know I want to go to grad school. I'm in the top 10 or so of my class, and consequently got invited to do this Accelerated Master's in Mechanical Engineering program. The program is basically a 3-2...
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    Momentum and mass balance in fluid mechanics

    If you're new to continuum mechanics, look up the Material Derivative. Applied to density, you can derive that first equation. You might use the Material Derivative to derive Reynolds Transport Theorem. Applying that to momentum, you can find the second equation, which is basically Newton's...
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    A flying skateboard possible?

    Adding on to what jedishrfu said, drag would also be a huge issue if you were "riding" it similarly to how one rides a skateboard. I think the best bet for a sort of human aircraft is the torso/back-mounted wings as it's the most centralized/stable/controllable way to mount equipment on a...
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    Min torque rating for a gear and pinion

    Each component has a maximum load rating -- make sure the load on each separate component does not exceed the rating and your design should not fail. You may also want to add a factor of safety to account for possible overloading.