Thanks for making this video. I really appreciate you going into detail about the solution for the second order diff. eq. Most physics lessons just give you the solution and don't derive it.
Good question! It goes back to the curious replacement of time derivatives with lambdas to form the characteristic equation at the beginning. The derivative of an exponential function is again exponential just bringing down and out the coefficient called lambda. As the differential equation is linear operation then you can sum various and just two serve to give a general solution, since the lambda1 and lambda2 they need to satisfy the characteristic equation if you think about it and of course there are 2 solutions to that. Hope you already found the answer.
Thanks for making this video. I really appreciate you going into detail about the solution for the second order diff. eq. Most physics lessons just give you the solution and don't derive it.
2:30 what happened to the 1/m in front of the radical? what m is in the denominator?
4:04 can someone please explain how he did he did that?
Good question! It goes back to the curious replacement of time derivatives with lambdas to form the characteristic equation at the beginning. The derivative of an exponential function is again exponential just bringing down and out the coefficient called lambda. As the differential equation is linear operation then you can sum various and just two serve to give a general solution, since the lambda1 and lambda2 they need to satisfy the characteristic equation if you think about it and of course there are 2 solutions to that. Hope you already found the answer.
th-cam.com/video/uI2xt8nTOlQ/w-d-xo.html pretty detailed explanation here
i don’t understand what has happened at that moment (4:10). why c1 and c2 with e involved?
That is the genearl solution of the DE and C1 and C2 are just constants to be determined when using the boundary of time limit conditions.
@@MichelvanBiezen thank you. i will learn DE next to understand this.
How to find c1 an c2 sir?
by inserting initial conditions
amazing explanation
from Brazil
Fala parça...
Why do we have the Euler's number in that equation?
That is the general form of the second order differential equation as depicted.
Yes, sure! Forgot that. Thank you.
GOAT