Simple Harmonic Motion Question

When finding the displacement-time function given the velocity-displacement function using integration, why do we assume v is positive?

EDIT: Question is in comments.

Question

Simple Harmonic Motion Question

When finding the displacement-time function given the velocity-displacement function using integration, why do we assume v is positive?

EDIT: Question is in comments.

anonymous · Answer

v^2=n^2(A^2-x^2)
v=n(A^2-x^2)^(1/2)

Why isn't v =+-n(A^2-x^2)^(1/2)

anonymous · Answer

$$v^{2}=n ^{2}(A ^{2}-x ^{2})$$
$$v=n \sqrt{a^{2}-x ^{2}}$$

anonymous · Answer

If you need even the direction of velocity,
then choose the sign depending on whether x>0 or x<0.

anonymous · Answer

But if you're just trying to find the displacement-time function, wouldn't your final answer be +- [the function]? But that wouldn't really make sense

anonymous · Answer

Yeah, if we consider the +ve sign and integrate, we get a trigonometric function which automatically takes care of sign.

anonymous · Answer

But depending on the sign, after we integrate, it will change to either arcsin or arccos...How do we figure out which one it is

anonymous · Answer

There should be some information of position and time, which can help us finding the appropriate function.

anonymous · Answer

A particle is moving with simple harmonic motion of period pi seconds and maximum velocity 8m/s. If the particle started from rest at x=a, find a.

anonymous · Answer

I got up to the step v^2=64-4x^2
but what do I do when I squareroot both sides? Do I put a +- or assume positive (like my textbook does). But why do you assume positive?

anonymous · Answer

Why don't you post it in physics? I will reply there..

anonymous · Answer

In Australia, motion is in mathematics for some reason haha :)

anonymous · Answer

That is good. :)
You can solve this way,
Use, $$T = 2\pi /\omega $$ 
where T-time period,
w- angular velocity.

Now, use the expression $$v = A \omega \cos wt $$
For maximum velocity. Got it?

anonymous · Answer

hmm but the book says to integrate to get an inverse trig function, and then rearrange the equation so its like x=[trig function]. Then you substitute t=0 in to find what a is

anonymous · Answer

Oh, then consider the positive sign. the sin or cos will take care of the sign.
anyway, the w above was angular frequency. sorry.

anonymous · Answer

okay! I think I kind of get it... Is it like you can use positive or negative, but whichever you use, the trig function will take care of it for you?

anonymous · Answer

in the question above though, you have to take v as negative though