Derivation Of Wave Motion With Complex Calculation

[Nishan]

When I find time I'll take you through a standard oscillator.

I would love to.

And will it solve my problem.

[exchemist]

I know that . I think you are not getting my question . I want to understand math . I have posted a picture of math in book " A textbook of Physics" above .

I want to know especially 

x= A1(coswt + i sinwt ) + A2 ( coswt - i sinwt )

  = (A1 + A2 ) coswt + ( A1i - A2i ) sinwt

  = A3 coswt + A4 sinwt 

here we supposed an imaginary number to be A4

   Again 

  A3 = a sin B

  A4 = a cosB

It shows that either cos B or A4 is imaginary .... Is'nt it?

then we do x = asin B cos wt + a sin wt cos B 

when cos B = imaginary then B is imaginary so is sin B

   then finally finding solution we do 

            x = a sin ( wt + B )

     which I thought should have been imaginary soulution . but it works well .

So I think I was missing something here . I ho[e you get me now. 

I am not sure your textbook is a very good one. The author (who seems rather obscure) does not seem to make it very clear what he is doing. There is a discussion of ways to solve the differential equation here: https://math.stackexchange.com/questions/1575291/how-to-solve-harmonic-oscillator-differential-equation-dfracd2xdt2-d

 

I think solution 2 is similar to what you have in your textbook.