Recent content by phymath7

Is the infinite series ##\sum_{n=1,3,5,...}^\infty \frac {1} {n^6}## somewhat related to the Riemann zeta function?The attached image suggest the value to be inverse of the co-efficient of the series.Is there any integral representation of the series from where the series can be evaluated?

That's what I mentioned in the statement. I found the least thickness to be 173 nm. So 25 nm is not enough to produce fringe pattern? What about if the width was 200 nm. Would that be enough to answer the question(what about the order of the fringe)?

Nope. Have a look at the book.

The context is the condition for constructive interference with thin film that is derived in the mentioned book of 5th edition.

As the value of cos##\theta_{t}## comes out to be greater than 1 so I tried to calculate the minimum value of d the thickness of film which turned out to be approximately 173 nm. Which clearly reflects the fact that the thickness is not enough to produce the fringes. Am I right? Is the question...

The simplest version I know: Energy supplied to the system is equal to the change in kinetic energy

I wonder how this can be explained by the work-energy theorem.

So if we set the damping constant ##\beta=0## that is if we consider an undamped oscillator the amplitude becomes infinity! What is the physical meaning of this phenomena? As we know energy fed into the system is proportional to ##A^2##. So does this mean that an infinite amount of energy is...

Does the 2nd postulate of special relativity imply that if I shift the origin of a co-ordinate system to make another(without rotation),only then the speed of light is constant in both reference frame but so is not true when I do the shifting with rotation?

Thanks. But a detailed work on this topic would be appreciated (from books or notes).

Yeah, I referred to vector components.

Does it violate the postulate of special relativity in any sense?

I need the relationship between ##\lambda## and ##R_2## which represents a hyperbola.How am I supposed to get that?

Did you write the explicit relation between ##\lambda## and ##R_2## ?Do you see how complex this one? I am afraid that it's beyond my (and even for those who are more advanced) capability to do the fitting.

The denominator "I" is the moment of inertia of the coil of galvanometer.