- #1
noranne
- 16
- 0
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?
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?