      # Derivation Of Wave Motion With Complex Calculation

mechanics harmonic oscillator

18 replies to this topic

### #18 Nishan

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Posted 30 June 2019 - 10:26 AM

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

I would love to.

And will it solve my problem.

### #19 exchemist

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Posted 30 June 2019 - 02:36 PM

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.stackex...n-dfracd2xdt2-d

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

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