Recent content by HeisenBerg46

Nice reasoning! Another way to solve it would be to ignore the physical aspects and treat the time derivative as a normal derivative. Granted the answer wouldn't be as accurate as yours, but it is possible and could be solved using Laplace transforms (although the physical component would be lost).

But you'd at least need values of x(0), x'(0), y(0), y'(0), z(0), z'(0) to use Laplace Transforms. Also, it would help to have a number in place of the variable a for a real-life problem.

Find the series representation of the antiderivative and sum it out until you see a correspondence in the two expansions.

Yes... I was looking for original problems with an answer, not just proofs. But to answer your initial problem, they correspond to the real part of the roots of the xi function, which are more easily calculated. These problems are very interesting though...

The answer really depends on which one you mean. Remember that the laplace transform of cos(a*t)=s/(s^2+a^2) for a real number a and s/(s^2+a) for complex s.

Which is e^(-2s) because the laplace transform of the unit step function with a step at c is e^(-sc). It works the same way with all step functions, and you can even find an approximate method for the dirac delta function.

The unit step function is zero until you reach c (the x coordinate of the first step) and after that, the lower boundary of the integral that is the Laplace transform can be restricted to c. If you factor out e^(-s*c), you are left with e^(-s*c)*L(f(t)) where f(t-c) is the function that the unit...

H(s)=*L(cos(3t)(s))=s/(s^2+9) because L(cos(omega*t)(s)=s/(s^2+omega^2) for real s and s/(s^2+a) for complex s

The Higgs Field is a great way to explain spontaneous gauge symmetry breaking which affects almost everything pertaining to the Universe and its origins. As far as I know, there is no other quantum physical way to explain the creation of the inhomogeneities that eventually expanded into the...

I am looking for extremely challenging math equations/problems to solve. I would appreciate any problems in any field of mathematics (almost nothing is too difficult). Note that I am looking for straightforward problems with an answer (not proving someone else's conjectures). Who knows, others...