Equipment Needed :

Statics Board

Mass and Hanger Set

Stopwatch (ME-1234)

Mounted Spring Scale

### Theory

Imagine a mass hanging from a spring. At rest, the mass hangs in a position such that the spring force just balances the gravitational force on the mass (its weight). When the mass is pulled below this original point (called the equilibrium position), the spring exerts a force to pull it back up. When the mass is above this original point, gravity pulls it down. The net force on the mass is therefore a restoring force because it always acts to accelerate the mass back toward its equilibrium position.

Previously you may have investigated Hooke’s Law, which states that the force exerted by a spring is proportional to the distance beyond its normal length to which it is stretched. (This also is true for the compression of a spring.) This relationship is stated as F=-kx, where F is the force exerted by the spring, x is the displacement of the end of the spring from the equilibrium position, and k is the constant of proportionality, calle dthe spring constant.

Whenever an object is acted on by a restoring force that is proportional to the displacement of the object from its equilibrium position, the resulting motion is called Simple Harmonic Motion(SHM). When the simple harmonic motion of a mass, M, on a spring is analyzed mathematically using Newton’s Second Law (and calculus), the period of the motion, T, is as follows:

The period, T, is the amount of time for one complete oscillation (down-up-down). In this experiment you will investigate this equation for the period of simple harmonic motion.

**The spring scale that we used was unfortunately too stiff to be used in the experiment. The oscillation was too short for us to measure proper values for the procedures. Therefore we couldn’t complete the experiment.