Q:

Sign convention in simple harmonic motion

I have noticed that velocity,acceleration and displacement ,all of them have a positive and negative values depending on their positions in an shm.Is there a sign convention for these terms.I will be glad if you can answer as my textbook fails to provide any information regarding this

A:

For simple calculation, let's assume our model to have the following displacement relation with time. 
$x=A\sin({\omega t +\phi})$ $\tag 1 $
On differentiating it,
$v=A\omega \cos({\omega t +\phi})$ $\tag 2$
From the above two equations,
$v^2=\omega^2 ({A^2-x^2}) $
$\therefore v=\pm \omega \sqrt{A^2-x^2} \tag 3$
Equation $(3)$ tells us that for a particular '$x$' we can have two directions of velocities. One when the block moves from eqm. position to amplitude and another when the block comes back to the eqm. positions from the amplitude.
For acceleration,
$a=-\omega ^{2}x$ $\tag 4$
$\therefore a = -\omega ^{2}Asin({\omega t +\phi}) \tag 5$
Equation $(4)$ tells us that for a particular value of '$x$' we can have only one direction of acceleration. The direction of acceleration always points towards the eqm. position. When the block is at the right of eqm. position it acts towards the left and vice versa. It should be taken into notice that equations $(3)$ and $(4)$
are general and apply to every case of SHM.

I didn't understand the acceleration part. Why does it have to point toward the equilibrium point ?

For spring-block SHM, the restoring force is given by,
$\vec{F}=-k\vec{x}$, where x is the position of the block from the equilibrium position (origin).
$m\vec{a}=-k\vec{x}$
$\vec{a}=-(\sqrt{\frac{k}{m}})^2 \vec{x}$
$\therefore \vec{a}=-\omega ^2 \vec{x}$
The restoring force always acts towards eqm position. When $\vec{x}$ is positive $\vec{a}$ is negative and vice versa. I hope this point is clear to you. 
The direction of the force is same as the direction of acceleration. If there is a force, there is acceleration. However, it doesn't necessarily mean that if a force is acting on a body, the body's velocity vector will be in the same direction. The force could be acting in the direction opposite to the direction of initial motion and keep depleting the body's kinetic energy and finally bringing it to rest and begin accelerating the body in its own direction. This is exactly what is happening here.

A:

The diagrams below define the positive x direction if $X$ is a positive quantity.

The sign convention is that right is positive (increasing distance $x$).  

A:

This table might help you:

Here, $x_1$ is the initial position of the spring and $x_2$ is the final position of the spring.

