- #1
Taylor_1989
- 402
- 14
Homework Statement
Hi guys, I am having trouble with ex 6.1 and 6.2. I am listed my ans below, and shown working. Could someone please advise. First I am not sure why I have to start with $$x=Ae^{imt}$$. Why cannot start with
$$Ae^{px}$$?
Homework Equations
The Attempt at a Solution
i) $$Aux: -m^2+irm+r^2=0$$
$$\Delta=(ir)^2-4(-1)(r^2)=3r^2$$
$$\sqrt(\Delta)=r\sqrt(3)$$
$$m=\frac{ir\pm r\sqrt(3)}{2}$$
$$x=e^{\frac{-ir}{2}}(Ae^{\frac{ir\sqrt3}{2}}+Be^{\frac{-ir\sqrt3}{2}})$$
ii) For this I followed the same process but came up with, which not enitrly sure if that satisfys the general solution.[/B]
$$x=Ae^{\frac{-ir}{2}}$$
iii) Once again same process and I got
$$x=e^{\frac{ir}{2}}(Ae^{\frac{ir\sqrt5}{2}}+Be^{\frac{-ir\sqrt5}{2}})$$
6.2 why do I have to concern myself with the solution, of
$$y=Axe^{imt}$$
when I am finding the P.I?