Transforming Equations for the Simple Harmonic Oscillator

[noranne]

I guess this is maybe more algebra than calculus, but it stems from a calculus problem, so I'll stick it here.

The problem is:

In the case of the simple harmonic oscillator the solution [to the EOM] may be written at least 3 ways

x(t) = Acos(wt) + Bsin(wt)
= Ccos(wt + del)
= De^(iwt) + Ee^(1wt)

Express C and del in terms of A and B. Express D and E in terms of A and B.

What I've got:

I got the first part, C and del, but I can't figure out how to find D and E. It seems relatively straightforward, I put the A/B eq as the LHS and the D/E eq on the RHS and just applied Euler's Formula to the D term. But I can't figure out how to get the E term in terms of cos and sin.

Any help please?

 

[Mindscrape]

Hint: A constant that has the imaginary unit in it is still a constant.

 

[noranne]

Yes, I know, but that still doesn't help me get E*e^(wt) in terms of cos and sin.

 

[Dick]

D*exp(iwt)+E*exp(wt) is NOT a solution to a simple harmonic oscillator problem in the region of the universe I'm used to. Are you sure you don't mean D*exp(iwt)+E*exp(-iwt)? You certainly can decompose exp(wt) into sin and cos. It's exp(wt)=exp(i(wt/i))=cos(wt/i)+i*sin(wt/i). But if w and t are real, those sin and cos aren't the oscillatory functions you'd expect.

 

[noranne]

Yeah, one of my friends just told me "Didn't you get Prof's email? That's a typo!"

Gr. I KNEW that I wasn't doing it wrong.

Thanks!