SHMotion Question (1 Viewer)

[roryclifford]

Hi Guys,

I am struggling with this question, thought I had nailed it but got the last part wrong and am unsure why, and the solutions are unclear.

A particle whose displacement is x moves in SHM such that accel = -16x. At t = 0, x = 1 and x (dot) = 4.

(iii) Find x as a function of t.

Before this part I had shown that |x (dot)| = 4 root (2 - x^2)
And shown the greatest displacement to be root 2.

I ended up with root 2 sin (4t + pie / 4)
However they have like 3 different solutions. Can someone do it and show me the working? Would much appreciate. And if that Goodwin guy trolls this thread just ignore him, the guy is attention seeking and childish.


Cheers! Hopefully it is not too unclear / long

 

[bleakarcher]

in these questionz can u quote v^2=n^2(a^2-x^2)

 

[bleakarcher]

v=4sqrt[2-x^2]=dx/dt
dt/dx=1/4[1/sqrt[2-x^2]]
Integrating w.r.t.x:
t=[1/4]*integral[1/[2-x^2]] dx=(1/4)sin^(-1)[x/sqrt(2)]+C
When t=0, x=1,
(1/4)sin^(-1)[1/sqrt(2)]+C=0
C=-(1/4)*(pi/4)=-pi/16
Thus, t=[1/4]sin^(-1)[x/sqrt(2)]-pi/16
Transposing:
x=sqrt(2)*sin[4[t+pi/16]]=sqrt(2)*sin[4t+(pi/4)]
and so u are correct

 

[apollo1]

im going to put it in latex for you hold on a second.

 

[AAEldar]

There you go.

 

[taeyang]

I got.....

 

[bleakarcher]

thanks AA, my first latex edited work

 

[apollo1]

ur right. i dont no how three solutions are possible.

 

[bleakarcher]

u can two solutionz lol, the other being in terms of cosine

 

[OldMathsGuy]

in these questionz can u quote v^2=n^2(a^2-x^2)

My understanding is that you cannot just quote that equation. Either it will be given to you and you will be told not to prove it, or you will be asked to derive it formally, or through the natural process of the question.

Best Regards
OldMathsGuy

 

[roryclifford]

Oh wow guys, sweet! Latex makes everything so much clearer.

Well the solution I got was out of the Success One HSC book, which had root 2 cos (4t - pie / 4) as the main answer with two other auxiliary solutions listed. I don't know, looks like I was right

Thanks a tonne! )