1) Which signal are you given? The Period is just the amount of time that a function repeats itself. For example has period because
2) Do you know the equation of the period of a pendulum? In the small angle approximation (which is the approximation that you're using) it is a very simple function of its length. Once you have the function that gives the horizontal position, their first and second time derivatives will give you the velocity and acceleration respectively. Because it is their definition, the velocity is the time derivative of the position, and the acceleration is the time derivative of the velocity.