where x, is the distortion of the SHO, F is the force it exerts, and k is an elastic constant for the SHO. A spring for instance is a SHO. A spring with a spring constant (k) of 2000 Newtons per meter distorted 0.5 meters, exerts a force of 1000 Newtons.

Each SHO has what is called a natural frequency. The natural frequency is the frequency at which the SHO oscillates when set into motion. The equation for natural frequency is as follows:

where m is the mass attached to the spring, and k is the spring constant.

The purpose of this experiment is to determine the theoretical natural frequency of a given spring, and then determine its natural frequency experimentally, and determine the error between the two. Another purpose is to determine the effect of the

frequency of the driving force on the amplitude of the mass’s oscillation. The hypothesis is that the experimentally determined natural frequency will be lower than the theoretical natural frequency. Energy is not completely conserved in this lab due to heat and air resistance; therefore the experimentally determined natural frequency will be dampened.

The graph shows a maximum at approximately 1.27; however, it should be around 1. This error is probably caused because the spring is not massless, therefore the ùd value is slightly higher than it should be. The trend line also approaches zero as the ùd/ù values vary from 1.27; it appears to asymptotic, as it should be, because the amplitude will always be greater than zero if force is applied and it decreases as the force varies from the natural frequency.

0.020 0.052 3.8 2.34 5 2.2 2.14 -2.25% 14

Next, a 20 g mass is hung from the spring again. This time the spring is at

Some topics in this essay:
Percent Error, Newtons SHO, Analysis Conclusion, Hooke’s Law, natural frequency, theoretical natural frequency, theoretical natural, determined natural frequency, experimentally determined natural, determined natural, experimentally determined, 0020 0052 38, frequency experimentally, natural frequency experimentally, spring spring, 0020 0052, spring constant, 5 22, determine natural,