For oscillations: omega^2 x amplitude = acceleration, i thought it should be acceleration=-omega^2xdispl, why?

Question

For oscillations: omega^2 x amplitude = acceleration, i thought it should be acceleration=-omega^2xdisplacement.
Is displacement always equal to displacement?
Where is the negative sign and when do we have to take into consideration the negative sign?

I totally cannot understand how the equations are used in the topic oscillations are used and i always fail with 0 marks cause i don't even know what formula to use, can someone please explain to me.

like i saw v=+/- (omega x square root of x0-x^2) what is x0?
and why i see another formula for velocity to be -x0sin(omega x t)
where t=time???

HELP, i can't understand and is suffering from a mental breakdown at the moment.

Please reply fast!!!

Edit:
Is displacement always equal to amplitude?
like i saw v=+/- (omega x square root of x0^2-x^2) what is x0?

There was some error while typing these two statements

Answer 1

In this case, amplitude and displacement are pretty much the same thing. A Simple Harmonic Oscillator will move back and forth an equal displacement in each direction with time. That is the amplitude. If you graph the displacement against time, you get a sine wave, and the maximum displacement is the amplitude of the function.
X0 is your initial value. It's a constant and it represents the displacement when you first started the oscillations.
There are two ways for finding the velocity. There is the function v=+/-(omega((x0)^2-x^2)^.5), where x0 is a constant as I stated above, and x is the displacement at that instant. Don't get confused by all the parentheses, it would look simpler if I wrote it out by hand. The other function is the function of velocity against time, which is v=-(x0)sin(omega x t). So if you know either the position, or the time of a particular instant, you can find the velocity of the oscillator by choosing either equation.

Answer 2

Dear Oscillation is a special type of movements,
the osculating body (that his move called oscillation) is move in the same path forth and back.
so it have at some point to have zero velocity, so it have special kind of acceleration.