Recent content by Piyu

Hmmm but the problem explicitly states express r(T) and v(T) in terms of r(0) and v(0). because for the next part we must find the value of ωT that shows a trapped particle. I could equate each of the coordinate at t=T with the one at t=0 but then ill still have to solve them simultaneously...

Wow didnt think of that trick thanks! I've applied it and gotten a much shorter term for z(T) and \dot{z}(T) However, to express r(T) in terms of r(0) ill need to merge all the terms together. but i cannot combine the terms together where r(T) = x(T) i + y(T) j + z(T) k. this is because...

Ok here goes then, For 0<t<T/2 2m\omega^{2}z=m\ddot{z} general solution for such a 2nd order differential is z= Ae^{\sqrt{2}\omega t}+Be^{-\sqrt{2}\omega t} z(0) = A+B \frac{\dot{z(0)}}{\sqrt{2}\omega}=A-B so A = \frac{1}{2}(z(0)+\frac{\dot{z(0)}}{\sqrt{2}\omega}) and B =...

Homework Statement A time dependent potential energy is given by V(r,t) = \frac{M}{2}f(t)\omega^{2}(x^{2}+y^{2}-2z^{2})where f(t) = 1 for 0<t<\frac{T}{2} and f(t)= -1 for \frac{T}{2}<t<T. and f(t+T) = f(t) Find r(T) and v(T) in terms of r(0) and v(0) Homework Equations F=-\nablaV The...

Hello, I am trying to derive the formula given in by . I understand we need to move it to the center of momentum frame to solve. Using the relativistic energy equations. I find that : E = E1 + E2 E1 = sqrt((Mc)2+(pc)2) E2 = sqrt((mc)2+(pc)2) where both have equal magnitudes momentum p since...

Ah icic, but how do i turn that equation to form the length contraction expression of L = L_0 / Y

Wow, i guess i was totally wrong in my understanding of the equation. Btw, how could i use this then to derive length contraction? In this case, the u will not be zero and hence it'll look like dx'=Y(dx - u dt)

Mind explaining it in abit more detail? I'll appreciate it. This part has been hurting my brains for the past few weeks and i still haven't been able to come up with a reasonable argument or mindset in assigning the t_0 and L_0 of time dilation and length contraction. All I've concluded so far...

But in any case, L_0 will still be dx while L is dx' isn't it? since the dx frame is the one that measures the proper length

Hello! need some help with length contraction. So according to lorentz transformation we got I don't know how to put symbols so ill use Y as gamma since they look alike :) dx' = Y dx - u Y dt So proper length refers to the frame where dt = 0 since u are measuring the ends at the...

Yeah so how come time dilation uses the observer as the proper time. This is the same as if we put a clock on the source frame that ticks with every frequency and the observer sees it going faster than the source itself. According to time dilation, should'nt the "tick" of each clock in the...

AH! So whenever i integrate over a variable like dx, it has to go from negative to positive(the right way). Never knew that :P Thanks for the help appreciate it!

NP glad to be of help :) Have a nice day! :P

V3, just apply the formula for potential between 2point charges, u got length x and height y. u can figure out the r using those. Sorry, thought u had trouble finding the work done. Erm i was going to use superposition of the 2 work done by working them out separately. Alternatively, u could...

Ah sorry, wasn't reading properly. Work done is charge * change in potential(Vfinal - Vinitial). V at final is set to be zero. (In fact we can just simply use the electric potential energy formula and subtract). Do the work done separately between the 2.7 charge and the 2 charges and add...