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How does one get the solution to the differential equation for SHM?

I understand the derivation for the simple harmonic motion equation: F = -kx ( in a 1-D case) acceleration = x''(t) = (-k/m)x so x''(t) + (k/m)x = 0 But why is the solution to this equation x = A cos...

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Voltage Difference Equation Terminology

For the formula for getting voltage difference [itex] V_b-V_a=-\int _a^{b} Edl [/itex] how do we know where the limit a and b go? In the equation it goes from a to b but why not b to a? For example ,...

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Hot Air Balloon Equation

I had meet a problem when I study the concept of the hot air balloon. The equation was giving Load = P*V*(1/TempAir - 1/TempBalloon)/R Then I reverse to TempBalloon = 1/[1/TempAir -Load*R/(P*V)] When...

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Biot–Savart Law

I'm not sure I get how:[tex]\frac{\mu_{0}}{4\pi}\int_{C}\frac{I(d\vec{l}\times\vec{r})}{r^{3}}[/tex] = [tex]\frac{\mu_{0}}{4\pi}\int_{C}\frac{I(d\vec{l}\times\hat{r})}{r^{2}}[/tex] the r is a...

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partition function: [itex] Z=Z_{kin}*Z_{pot} [/itex]

Hey, If I have a canonical partition function with: [itex]Z=\frac{1}{h}Z_{Pot}\cdot Z_{Kin}[/itex]. Can i callculate immediately the average potential Energy, by:...

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what is electric flux

The defination of electric flux on wiki is "is the rate of flow per unit area of the electric field. Electric flux is proportional to the number of electric field lines going through a virtual...

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fractional energy loss per cycle in a heavy damped oscillator

http://www1.gantep.edu.tr/~physics/m...2/chapter2.pdf On page 9 and 10 of the above PDF the method for deriving the fractional energy loss per cycle in a lightly damped oscillator is described. I...

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Reflection of sound depends on frecuency?

Hi! I need some help understanding something related to sound. I am currently studying a book called Sound Propagation. An Impedance Based Approach, by Yang-Hann Kim. There is a part where he talks...

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What power supply (amps) would run this plasma globe optimally?

It says DC in 12volts but I'm not sure how many amps this thing can handle... I don't want to plasma myself so I was looking for helpful answers, thanks guys pic of globe (paid $8 not bad)...

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Flux through a closed surface

Hi, I'm trying to teach myself electricity and magnetism (and it's not easy!) and I'm not sure I understand flux... For one thing, why is the flux through a closed surface zero if there is no charge...

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Thermodynamics: Heat absorption / rejection vs colour

I am working on an automotive project and am looking to pick up any gains that I can. In doing so, I've been studying the effect that colour has on thermodynamic characteristics. To be specific, I am...

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Griffiths Electrodynamics gradient of charge distribution

I do not understand the following from Griffiths’ Electrodynamics – page 424 Equation 10.21. [tex] \nabla p = \dot{p} \nabla {tr} = … [/tex] I’m not sure how much of this applies (I think my question...

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Elastic collisions proof

Suppose that a mass M1 is moving with speed V1 and collides with mass M2 which is initially at rest. After the elastic collision they make, both momentum and kinetic energy are conserved. [tex]...

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Why are astronauts weightless?

If they're orbiting Earth, then they're in uniform circular motion. And if they're in uniform circular motion, then they experience a centripetal force (and thus centripetal acceleration) towards the...

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Series and parallel circuits

Hello, I was curious, if two resistors are separated by a battery (i.e. a circuit looks like battery -> resistor -> battery -> resistor), are the resistors in series? Similar idea with a...

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How to handle negative momentum

We have a variable-inertia flywheel coupled by a shaft to a fixed inertia flywheel. The VIF (variable-inertia flywheel) has a moment of inertia range of 10 to 5 (m2*kg) and an initial velocity of 100...

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Banked curve curcular motion

hello good morning. Let look at the two diagram. (back view) In STATIC, a car is remauning static at a bank curve and its force diagram is as follows. for this case, the normal force is smaller than...

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carnot cycle

I am thinking about the adibatic compression when the gas gets back to Th from Tc... My question is how the p and V gets same as the initial pressure and temperature... Can you prove it?

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Questions on classical mechanics

Hi Question 1 i was wondering if there is any method to find the point from which the angular momentum is a conserved quantity. let me e.g. choose the case of a planet moving in an orbit around the...

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Suppose you are far into deep space

You are accelerating at constant acceleration without anything physically touching you. Do you feel anything? What would an accelerometer read if the same force is applied to the accelerometer without...

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