General Form query (1 Viewer)

[Bi0mic]

Hey all ...

Heres what really is a simple question, but a lack of understanding of the concept - it comes from 2002, Q4c(iii):

A Particle, whose displacement is x, moves in SHM such that acceleration=-16x. At time t=0, x=1 and v=4

the question moves on asking to prove its velocity and find its amplitude then iii requires to write "x as a function of t. You may assume the general form of x".

Ok fair enough, x=acos(nt+@), the formula ends up being x=(sqrt 2)cos(4t+@) .. (where only the 2 is square-rooted)

To find @, the text progresses to substitute x=1, t=0 (as given in original question) to find that "cos@=1/(sqrt 2)" and then by differentiating the x formula providing the following velocity formula: v=-4(sqrt 2)sin(4t+@), followed by substituting in v=4, t=0 comes out with "sin@=-1/(sqrt 2)"

My question is this, how do you know which value of @ to take? ... as one gives me +pie/4 and the other gives me -pie/4

Thanks all .. i hope this is readable .. lol .. again, for those playing at home this is Q4 c(iii) 2002

Cheers

 

[jumb]

In simple harmonic motion, they are both the same. The question will usually ask something like "First time After t=0". Id go with the first one after t = 0 for this question, or jsut write both as theyre both correct.