[DampRobot]

To calculate the force which the string being pulled down upon can see, look up the stall torque of the motor you're using. This should be in Nm, in*Lbs, or some other distance times a force, so when you divide the torque (lets say in Nm) by the length of the arm you're using (lets say in meters) you get the force exerted by the motor (in this case in newtons).

The force downward is related to the angle the arm of the motor makes with the vertical by a sin function.

How far the string gets pulled downward depends on what it's connected to, but if it's just connected to a fixed object, the distance it gets pulled downward will involve the spring constant of the string and it's length. Basically, you're going to want to find the distance the string gets pulled where the force of the motor (equal to sin(theta)*torque/arm length) equals the spring constant K times the length the string has been pulled. Keep in mind that theta and the distance the string has been pulled are related, and solve algebraically.