Displacment in simple harmonic motion after periodic time

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i just studied S.H.M and i am wondering is the displacement equals the amplitude or zero after the periodic time?
because when i thought it equals zero at first because the periodic time is time required for the object to make acomplete oscillation and return to it's starting point right?

but when i put the law T= [tex]2\pi\ \sqrt{m/k}[/tex]
T= [tex]2\pi\ *\sqrt{m/f/x}[/tex]

T= [tex]2\pi\ *\sqrt{m/mg/x}[/tex]

T=[tex]2\pi\ *\sqrt{x/g[/tex] (and unless the periodic time of every S.H.M is 0 this cant be right )

and no this isn't home but i asked the tried to ask the teacher and he didnt have time to listen.
And this is like my first lesson in S.H.M so i dont understand it that much.
maybe i didnt understand the periodic time right or something like that

also since y = A Sin (wt)
y = Asin ([tex]2\pi/T\[/tex]*T
y = Asin([tex]2\pi[/tex]=0
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Homework Helper
Well if you start at max displacement then your equation for SHM will be of the form

if you start at zero minimum displacement, it will be of the form y=Asin(wt)
But i still dont understand
if we try to calculate T
then we are trying to calculate the time the displacement reach 0 right?
so if the displacement is 0
T =[tex]\sqrt{Y/g}[/tex] right so if Y is zero wouldnt the T always be 0?(for the displacement i can use symbol X or Y right?)
isnt it from hook's law
that f=x*k
so k= f/x
so i putted that value in the law for the periodic time
and i got T = root of x / root of g

Edit: i am really new to simple harmonic motion and i am not very good at physics therefore i am trying to understand the laws better but i still don't understand the concept of S.H.M
what i know of it is that its a motion of an object where the acceleration increase with the displacement but in the opposite direction and that oscillation is when the object goes through the max displacement to the right then to the left then return to where it started and the time for that is called the periodic time.

and that the object move with an angular speed (omega) which is the magnitude of the angular velocity which is measured by radian and it decrease when the acceleration increases.
and that the acceleration reach's it maximum when the object reaches the amplitude while the velocity become 0 and velocity reaches its maximum when the object return to it's starting place.(this is all i know about simple harmonic motion but i am trying to calculate T by displacement but always get zero as an answer)

these are the only laws i know
w =[tex]2\pi\ /T[/tex]
T=[tex]2\pi\ *\sqrt{m/k}[/tex]
(fmax =k*A. i dont know if that is alaw since it isnt written in my book but it make since the returning force increase with the displacement it should be at max at the amplitude right?)
But i am trying to put alaw to combine the periodic time and the displacement but i cant do that.without always getting zeros

So i want to know what i am doing wrong any one can help with that?
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I don't really need some one to form the law for me i just want to make sure that the laws and info i have are correct and maybe little advice on where to begin

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