Constant Definition and 1000 Threads

Completely new to this and wondered if someone can explain what the correct equation of motion is if x is extension, t is time and a,b are constants x = b log (at) x = a t exp(-b t) x = exp(-b t) sin(a t) x = a sin(t)/b

##x^2(3x^2+4x-12) +k=0## ##(3x^2+4x-12)= \frac{-k}{x^2}## or ##(4x^3-12x^2)=-k-3x^4## ##4(3x^2-x^3)=3x^4+k## ##4x^2(3-x)= 3x^4+k## or using turning points, let ##f(x)= 3x^4+4x^3-12x^2+k## it follows that, ##f'(x)=12x^3+12x^2-24x=0## ##12x(x^2+x-2)=0## ##12x(x-1)(x+2)=0## the turning points...

I've worked through it doing what I thought I should have done. I normalized the original wavefunction(x,0) and made it = one before using orthonormality to get to A^2(1-1) because i^2=-1 but my final answer comes out at 1/0 which is undefined and I don't see how that could be correct since A is...

For a double integral, we might treat the "inner integral" separately and be able to compute something like ##\int_{x_1}^{x_2} f(x,y) dx## by holding ##y## constant during the integration. The same technique is applied in other places too, like for solving exact differential equations. I haven't...

Is the phase factor in : ##e^{i\phi}\Psi(x)## a constant or a global phase factor called ?

the attached files are a diagram of the circuit. also I believe I figured out how to proof equation (7) but I'm lost on how to proof (8)

Hi All, I'm doing research in magnetic nanoparticles that are coated with chain molecules (oleic acid, I believe) and I am trying to model these molecules' effective spring constant. The basic scenario is this: When a water-based ferrofluid is evaporated, it leaves behind only dried...

I know the amazing thought experiment by Albert Einstein with the two light clocks. (The observer at the train station has a light clock and the person in the train.) It's amazing because you can even deduce the formula to calculate how fast the clock in the train goes. But this experiment...

Hello folks, I am working on Java program just for fun to model an n-body problem using 3-dimension graphics. I'm looking for a way to speed up the model. Suppose for example that I decide to increase the speeds of all objects by a factor of, say, 2. To compensate, I would also increase the...

Hello folks, Not strictly a homework question, but thought this might be the best place for it. If I determine (experimentally) two values for some constant k, is there a simple meaningful way to state their (percentage) agreement. For example, imagine I carry out two different experiments and...

i. the threshold frequency; 3.9x10^14hz? it appears the line intersects at 3.9ii. the work function of the surface; 6.626x10^-34x3.9x10^14= 2.58414 × 10^-19J iii. Planck's constant unsure

Summary:: not constant spin How could I calculate the system lagrangian in function of the generalised coordinates and the conserved quantities associated to the system symmetries? I've been struggling for the case with not constant angular velocity, but I don't realize what I have to do...

I'm watching this video to which discusses how to find the domain of the self-adjoint operator for momentum on a closed interval. At moment 46:46 minutes above we consider the constant function 1 $$f:[0,2\pi] \to \mathbb{C}$$ $$f(x)=1$$ The question is that: How can we show that the...

Which one does it mean: "phase velocity" or "group velocity" or "speed of the wave front"? In the postulate of constant speed of light .

Isn't the meaning of speed, a variable of distance divided by a variable of time? Therefor isn't the meaning of a constant speed of light, a constant distance divided by a constant time? If there is any truth in this saying and there probably isn't, then what is the meaning of light constant...

If i am moving away from an object at a certain constant speed close to the speed of light, is that object also moving away from me at the same constant speed?

I'm reading the online version of a book that says Rindler observer comes right into my mind when I read this. So I think the book is wrong. What do you all think? On a second guess, perhaps the author takes the view that SR is only for constant speeds in the same sense that one could say that...

Please refer to the image

If ##N## is constant (per the partial derivatives definitions/ the subscripts after the derivatives) then ##G## is constant ##H - TS = constant## Taking the derivative of both sides with respect to ##T## while holding ##N,P## constant we get the following with the use of the product rule...

Q=heat capacity calorimeter*(-)change in T*moles =0.009089mol*-6.8C*4.38kj/C =-0.2707kj/mol This answer is wrong but it was the only one I could come up with right now. I just noticed units in the answer would be wrong too. Any suggestions?

I tried this but I don't know if it makes sense: Average velocity from A to B = 22/2 = 11m/s Average velocity from B to C = 104/4 = 26m/s (26-11)/6 = 3.75m/s

I am confused why the acceleration doesn't point to the center of the ellipse or one of the focus, since it moves in circular motion. Shouldn't the acceleration be just in the radial direction

Noether's theorem tells us that an invariance of the Lagrangian yields a constant of motion. In this problem, that constant is: $$Q_v = p^a \Big( \frac{\partial q_a^{\lambda}}{\partial \lambda}\Big)_{\lambda = 0} + p^b \Big( \frac{\partial q_b^{\lambda}}{\partial \lambda}\Big)_{\lambda = 0}=...

I solved this question until the end of the "c)Find the distance until the boat completely stop" However I can not solve the integral I encounter in the solution of the last part of c). Would you please check for math and maybe my mistakes and tell me what to do? Here:

Alright my idea is that, in order to show that ##f_i(q_i, p_i)## is a constant of motion, it would suffice to show that the Hamiltonian is equal to a constant. Well, the Hamiltonian will be equal to a constant iff: $$f(q_1, q_2, ..., q_N, p_1, p_2,..., p_N) = \text{constant}$$ Which is what...

Here is the Q below I want to see if my values for part b) is okay? This is what I have tried: Any help would be nice! Thanks

Good afternoon,I am preparing a laboratory report on the study of the oscillations of a spring and the following questions have arisen:The script asks us to represent the mass against the squared period, in this case, the slope will correspond to the spring constant divided by 4Π^2 and the...

It has been proposed the Hubble tension can be solved if we assume our galaxy is located in a giant void (such as KBC). I am confused at this point. If we were living in a giant void, we should have measured the Hubble constant lower. Since when the light passes an underdense region it gets...

If I have a sum ##f(x) + g(x) = c##, with ##c## a constant, does this imply that both ##f(x)## and ##g(x)## are also constants? If I just solve this equation for ##x##, I will find some values of ##x## which satisfy the equation. However, if I require that the equation be true for all ##x##...

##x(t)=x_m e^{\frac{-bt}{2m}}cos(ωt+φ)## Damping Factor: ##e^{\frac{-bt}{2m}}## (##b## is the damping constant) Estimated ##ω##: ##\sqrt{\frac{k}{m}}## More Accurate ##ω'##: ##\sqrt{\frac{k}{m}-\frac{b^2}{4m^2}}## Also: ##T = \frac{2π}{ω}## and ##F = kx##. So, my answers: ##k = \frac{Mg}{4x}##...

Initially we are given the statement Vav = (x-x0)/t, so far so good. But, we encounter the following paragraph... "We can also get a second expression for Vav that is valid only when the acceleration is constant, so that the v-t graph is a straight line (as in Fig 2-14 - [I've omitted the graph...

Summary:: What if you were calculating the voltage potential for a dipole, but underwater? I'm making a predictive model (in R programming) for the voltage potential at any point around a dipole. I need to be able to change parameters, one being the k constant. V=( kpcosѲ)/(r^2). Where V is...

NOTE: Sorry for my english. I use Google Translate! Comparing the performance with a friend of mine who is passionate about physics (and he is studying it by himself) we came to the same conclusion. In other words, we have calculated the time taken by both riders to reach the finish line. From...

Attempt: I was thinking of finding the slope of the graph but I only know the values for x = 10, y = 3 and y = 0. And without the y-intercept, I don't know the work function and can't solve for h. If you can't see from the picture, the last co-ordinate is (10,3) and the x-axis is measured in f...

Let f1, f2: {0,1, ..., 24} → {0,1, ..., 24} be such functions that f1 (k) = k + 1 for k <24, f2 (k) = k for k <24 and f1 (24) = f2 (24) = 0. Let gi1, i2, ..., I am (k) = fi1 (fi2 (... fim (k) ...)) for i1, i2, ..., im∈ {1,2}. Find the largest m for which irrespective of the selection i1, i2...

I can see why it would be pretty illogical to speculate that physical constants change over time, but is there more to it than just being 'illogical' to assume otherwise? Is it axiomatic in physics to presume certain physical constants are constant, because otherwise stuff like atoms and things...

In Barbara Ryden's introduction to cosmology book its written that "Introducing ##\Lambda## into the Poisson's equation allows the universe to be static, if you set ##\Lambda = 4\pi G\rho##" Then later on, in the book energy density of the ##\Lambda## defined as ##\epsilon_{\Lambda} =...

This paper just came out with a new measurement of the Hubble constant based on the technique of gamma ray attenuation. The result is consistent with the lower (CMB-based) value. Interestingly, they also do a joint analysis of several non-CMB techniques (BAO+BBN+SN+γ-ray attenuation), and find...

I've been attempting to solve this problem for three days now. I have thrown away my old attempts (like, scrumpled up into the bin), but my old attempts involved: Trying to set up simultaeneous equations relating the journeys between EH and FG to find the deceleration, but the reason why this...

In the first question should I remove the delta and put d or that doesn't make a difference and on the second question should I substitute the values of R, K, Cv and Cp or that's not required I'm not really sure how correct is my answer to the second question

So I was looking for some rate constants for a certain reaction and I found these: So I wanted to try them. The problem is, I have no idea how to correctly write the rate constants. Reactions number 1 to 6 is a no-brainer as it's simple Arrhenius. My problem is for rate constants 7 to 12. I...

Hello All. I am mentoring a high school student in my area with his class project for school. He has chosen he wants to launch an object (in our case, a softball) into a 5' diameter area. The idea is to build basically an oversized slingshot using an extension spring as the source of energy. We...

I was introduced to the concepts like molarity, molality , mole fraction, formality, normality etc. during general chemistry and it was said that these concepts are used to measure the concentration of solutions. But as the thing called Chemical Equilibrium came I was surprised when I read "In...

Okay so, recently I got a job with my local newspaper delivering newspapers to make some money while deciding how I want to continue my educational career (I already have some college under my belt but I'm taking a semester off). All the newspapers have to be at the houses by 6 am so in order to...

##-Fr=m.a## ##-cv^2=m.a## ##-cv^2=m.\frac{dv}{dt}## ##dt=-\frac{m}{cv^2} dv## After integrating, I get ##t=\frac{m}{c.v}-\frac{m}{c.v_0}## Then, solving for ##v## we get ##v=\frac{m.v_0}{v_0.t.c+m}## ##\frac{dx}{dt} = \frac{m.v_0}{v_0.t.c+m}## After integrating that, I get an expression for...

Ok, I have actually found the answer from http://www.bristol.ac.uk/phys-pharm-neuro/media/plangton/ugteach/ugindex/m1_index/med_memb/file/Nernst1.htm. Basically, a convenient way to analyze these equations is to take the log of both sides. Since e takes the natural log and the equations are...

I am doing a STEM project where we need to make a timer without any chemical reactions or electricity, and I think the best way to do this is to create a constant flow for a certain amount of time and weigh how much water comes out. What is the best way to create a constant flow of water for...

Hi, recently I got interested with practical applications of Newton's law of cooling. Its main disadvantage is that one has to measure temperature at some point of time (other than ##t=0##) to obtain solution for any other ##t##. However I've found an online calculator...

I thought the ratio was purely 4, because Helium's Z = 2 (atomic mass). Apparently this is not true, and now I'm stuck... I think there must be some other form of equation for the rydberg constant that is more general, but google and wikipedia are not helping that much. Any thoughts?