simple harmonic motion proof help (1 Viewer)

[kpq_sniper017]

actually, expressing it in the form:
x"=-n²(x-b) isn't sufficient.
u have to write a couple of extra steps:
let X=x-b
.'. X"=x"
.'. X"=-n²X, which is the defining equation for SHM.


btw. with x'2, u can write x^2...or even better, write: < sup >2< /sup > to change the 2 into a superscript (but delete the spaces between the tags)

 

[mojako]

actually, expressing it in the form:
x"=-n²(x-b) isn't sufficient.
u have to write a couple of extra steps:
let X=x-b
.'. X'=x'
.'. X"=-n²X, which is the defining equation for SHM.

don't really get what you did to move from the first .'. line to the second...
But I guess you're saying that we need to show that it's X"=-n²X, but I don't think you do...

 

[kpq_sniper017]

don't really get what you did to move from the first .'. line to the second...
But I guess you're saying that we need to show that it's X"=-n²X, but I don't think you do...

whoops. sorry.
i made the edit in my last post....looks ok now.


if u need further explanation, feel free to ask.

 

[mojako]

yeah I understand now... took me a fair while though
are you sure you need to do that?

BTW part B of the syllabus does say:
Extension to the case
x = b + a cos (nt + a)
and the corresponding equation
x'' = –n² (x–b)
describing simple harmonic motion about the position x = b.

(part B is where they give explanations and notes on syllabus dot pts, which are n part A)

And from a few questions that I did together in class, my teacher doesn't convert that to X'' = -n²X

And it's quite obvious that the "curve" of x'' = –n² (x–b) is just a kind of translation of x'' = –n² x (by b to the right). shiftting the x'' axis will make it x'' = –n² x.

 

[kpq_sniper017]

well, if it were me, i'd rather just write in the extra couple of lines. if u have a strict marker, it may get u the extra mark. it came up in a recent physical apps assessment that i did. i did the substitution and got full marks, and the teacher gave us worked solutions which also included the substituion X=x-b.

it's probably best to stick to the extra few steps "just in case".