Differential Equation - Introduction (4 of 15) The Solution of a Differential Equation - Ex. 2

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In this video I will give an example of a solution to a typical differential equation.

Next video in the Introduction series can be seen at:

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you have been instrumental in learning more optics and photonics

you da man much respect

Bass

that was so helpful. I had seen the formula for simple harmonic motion and the one or angular frequency but I didn't understand the relationship when my physics book explained it in words. this video helped me make the connection.

TheDeltaboss

WOW! Never saw it done like that! Great! 👍

curtpiazza

what a coincidence.. I am seeing this video for the first time and it is SPRING in Michigan.. and gee, doesn't this problem look familiar in regards to a SPRING and a MASS... :D .. excellent demonstration...

ptyptypty

you choose arbitrarily the func Acosωt asd a solution of the given diff equation, how do you know that?

chrysovalantistasiopoulos

Did anyone else catch the paranormal activity on the left side of the board at 0:37

rumpelforeskin

Sir Michel, is this topic under Mechanical/Electrical Vibrations: Undamped Free Vibrations??? Because the formula given on a video looks similar with mu"(t) + ku(t) = 0 from which according to my notes, the general solution would be u(t) = Acosωt + Bsinωt...

minjinseo

is the A in the solution an arbitrary constant? or is there a way to get a value of it?

jerardang

do i have to have say x=acos(wt) why not X=acost(Bt).
you get same result but with b=sqrt(k/m).
is k acceleration ? from using ure 2 video from your website you say that f=ma then ma=-kx. where x = length

Many thanks

ajj

x could also be an exponential function, isn't it?
if x = exp (sqrt(-l/m)*t)
dx/dt = sqrt(-l/m) * x
d^2x/dt^2 = (-l/m) * x

lordleoo

y′′+ky=umg sir, I need a solution to this D.E

quantumjourneyman

why do you multiply Acos(wt) times the radian w

adriankozubal

Why are we getting the value of w? arent we suppose to find x?

chriswass

I don't know anything about oscillation, would it be wrong if I exclude the constant from the solution? thus letting x just be cos(wt)?

procrastmh

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