Tim_Lou Posted February 15, 2005 Report Share Posted February 15, 2005 consider the oscillation of a pendulum...the angular acceleration of the system is d^2(angle)/dt^2= - g sin (angle) / Lso, basically, f''(x) = A sin (f(x)), is there a solution for such equation? edit: i forgot the negative sign... fixed Link to comment Share on other sites More sharing options...
sanctus Posted February 15, 2005 Report Share Posted February 15, 2005 ususally you solve this equation using the fact that for small angles you have sin(x)=x and then you got a normal differential equation. Now if there is as well a solution without approximations I don't know. Link to comment Share on other sites More sharing options...
Tim_Lou Posted February 15, 2005 Author Report Share Posted February 15, 2005 yeah... but if the angle is greater than pi/2, the approximation fails badly....hmm, is there other approximation for large angle? Link to comment Share on other sites More sharing options...
Bo Posted February 17, 2005 Report Share Posted February 17, 2005 no there isn't...The only way to solve the equation is by the method sanctus gave. btw if you want larger angles, you could of course expand the sine further (x-1/3!x^3+1/5!x^5...) So one of the first physical equations you'll learn (at least i did...) period of an oscillator=sqrt(length/g) is a poor estemination. Bo Link to comment Share on other sites More sharing options...
Tim_Lou Posted February 17, 2005 Author Report Share Posted February 17, 2005 no wonder why! i searched the internet for 2 hours and got nothing :( hmm, if the equation is expanded using sine...f''(t) + g/L ( f(t)-f(t)^3/3!x+f(t)^5/5!...) = 0, seems even more complicated... Link to comment Share on other sites More sharing options...
Bo Posted February 18, 2005 Report Share Posted February 18, 2005 nobody said it would be easy :o i think you can solve this by replacing f with the expension of the exp.(and then determine the coefficients) Bo Link to comment Share on other sites More sharing options...
IrishEyes Posted February 18, 2005 Report Share Posted February 18, 2005 BO-You're gonna have to tell us where you've been. We've been worried.No matter though, it's good to see you back!! Link to comment Share on other sites More sharing options...
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