Recent content by KateyLou

Homework Statement I have coursework on rhe convolution integral, however i am struggling to find the equation of motion to start the whole thing off with. I will attach a picture of the problem, is is simply a cantilevered bar with a concentrated mass on the end and a damper. Homework...

have had another go at this, and still cannot work out the first bit - the random removal of O(e^2) in some places and not others :-(

Homework Statement Taking e to be small, we have been given these two formulas to prove m1 = \frac{-1+\sqrt{1-4e}}{2e} = \frac{-1+(1-2e+O(e^2))}{2e} = -1+ O(e) m2= \frac{-1-\sqrt{1-4e}}{2e} = \frac{-1-(1-2e+O(e^2))}{2e} = -1+ O(1) Homework Equations The Attempt at a Solution...

oooh \int-e-4tsint=(16/17)e-4t((1/4)sint+(1/16)cos)) or \int-e-4tsin=e-4t(4sint+cost) YAY that what the answer sheet says

\int-e-4tsint=[(1/4)sinte-4t+[(1/16)e-4tcost+(1/16)\inte-4t (-17/16)\inte-4tsint=e-4t((1/4)sint+(1/16)cos)) Not sure what to do now?

Homework Statement Integrating -e-4tsint Homework Equations Our tutor suggested we did this by integrating by parts in a cyclic fashion and things would cancel out The Attempt at a Solution Taking u = sint t; thus u'=cost And v'=-e-4t; thus (1/4)e-4t \int-e4tsint =...

i am not too sure what induction is...(sorry!) guessing a form for an - do you is this not given by the recurrance relation?

Homework Statement Obtain the recurrene relation between the coefficient ar in the series solution y= (between r=0 and \infty) \Sigma arxr to (1-x2)y''-2xy'+k(k+1)y=0 Deduce that if k is a positive integer, then ak+2=0, so that the equation possesses a solution which is a polynomial...

oh! lol! Thank you guys :-)

ha! ok! So what is this definition then? I think i shall go an google it...

i don't know what definition i am using... I have taken that straight from the maths notes we were given... (sorry!) What do i know about the dirac delta function...well, the intergral of it is one, and that happens at t=0?

Right i have now completed this up to the last stage - i do not understand how it has gone from F(0) to \int_{-\infty}^{\infty} \left(\delta (t)F(t)\right)dt

Yes i think I get the =0 part (by the way how do you write equations like that?) And thank you re: the product rule - not sure how i managed to miss that! will go back to it and see how far i get this time!

Homework Statement Hi there, i am trying to do a proof that H'(t)= δ(t) Homework Equations We have been given the following: F is a smooth function such that lim (t-->±∞)F(t)=0 Therefore the integral between ±∞ of [H(t)F(t)]'=[H(t)F(t)]∞-∞=0 I understand it up until this point...

YAY! Thank you!