How do we find the period without using the amplitude?

[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.

 

[SammyS]

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.

Hello Shinaolord. Welcome to PF !

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

Also, show us how you are getting your results.

 

[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?

 

[SammyS]

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?

If a_max = Aω², then it should be true that v_max = Aω .

( a_max and v_max should both be positive. )

Doesn't it follow that ω = a_max/v_max ?

 

[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"

 

[Shinaolord]

Never mind I see

Sorry for do, my iPad won't let me edit

 

[SammyS]

Yes, correct, but for period the back of my book says t=v[max]^2/a[max].

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 $\displaystyle \ T=2\pi\frac{v_\text{max}}{a_\text{max}}\ .$