Homework Help: Finding Period from a and v

1. Mar 7, 2013

Shinaolord

This question has me completely baffled. So here it goes:

A spring oscillates with a period T and an Amplitude A. Solve for period and amplitude in terms of a[max] and v[max]

My math always comes out with an answer I know is wrong. Can anyone be kind enough to assist me?

Much appreciated.

2. Mar 7, 2013

SammyS

Staff Emeritus
Hello Shinaolord. Welcome to PF !

You really haven't given us enough detail to help.

Also, show us how you are getting your results.

3. Mar 7, 2013

Shinaolord

That's literally all it gives you. It says to "solve for the amplitude and period in terms of a[max] and v[max]. It's purely conceptual, which I think is the hindrance. Does that Help?

EDIT: Thank you for the welcome! Much appreciate, SammyS.

My results, via Algebra and substitution, is as follows:

a[max]=Aw^2, so A=a[max]/w^2
and V=-Aw, so V also =-(a[max]/w^2)w
which simplifies to v[max]=-(a[max]/w)
now, w=2[pi]/T, so v[max]=-(a[max]T/(w[pi])
so T=-v[max]w[pi]/a[max]
This doesn't seem right...Is my math or reasoning wrong? Am i just not seeing it?

Last edited: Mar 7, 2013
4. Mar 7, 2013

SammyS

Staff Emeritus
If amax = Aω2, then it should be true that vmax = Aω .

( amax and vmax should both be positive. )

Doesn't it follow that ω = amax/vmax ?

5. Mar 8, 2013

Shinaolord

Yes, correct, but for period the back of my book says t=v[max]^2/a[max].
This is all new to me, apologies if I seem "stupid"

6. Mar 8, 2013

Shinaolord

Never mind I see

Sorry for do, my iPad wont let me edit

7. Mar 8, 2013

SammyS

Staff Emeritus
That looks more like amplitude than period.

$\displaystyle \frac{v_\text{max}^2}{a_\text{max}}=\frac{A^2 \omega^2}{A\omega^2}=A\ .$

Whereas we had   ω = 2π/T .

So, if $\displaystyle \ \omega=\frac{a_\text{max}}{v_\text{max}}\,,\$ then $\displaystyle \ T=2\pi\frac{v_\text{max}}{a_\text{max}}\ .$