N otes on Chapter 9 A
pp 93 - 96 of your lab book

A mass on a spring is a simple, yet important physical object. Many behaviors can be modeled by using combinations of this simple object. With that in mind, we are going to investigate natural oscillations of a spring system.  

• The natural frequency of a system is the frequency at which the system "likes" to oscillate at. It is the frequency at which systems will oscillate in the absence of damping or driving forces.

A system oscillating at its natural frequency is the simplest possible case, and so such oscillations are called simple harmonic motion (SHM). The pendulum also exhibited simple harmonic motion, and it also had a natural frequency. We measured the period of the pendulum, and we could have easily calculated this natural frequency. Period is related to frequency by the simple relation:

f = 1/T

We will again measure the period of a system, but this time we will measure the period of a mass on a spring. The frequency of a mass on a spring is given by the equation:

 

Unfortunately, the situation we will measure in class is a little more complicated than this. Instread of a spring streched out horizontally, we will use a hanging vertical spring. This means that the mass of the spring itself will be a factor. To handle this we will replace the mass m with the sum (m + m _e ) where m_e accounts for the effect of the spring having some mass.

Procedure:

1. Static Measurement of k: 
1. Adjust the apparatus such that the bottom of the spring is exactly 1 m from the floor. This is the unstretched position.
2. Hang the 50 g mass with the hook on it on the spring.
3. Measure the distance from the unstretched position to the new position (at the bottom of the spring, not the mass)
4. Repeat steps 2 and 3 for masses 100 g, 150 g, 200 g, 250 g, and 300 g.
5. Plot the Spring Force versus the distance measured. (The spring force is -(weight) = -mg)
   
2. Measurement of the period as a function of mass
1. Again hang 50 g on the spring.
2. Stretch the spring a few centimeters.
   
3. Observe the oscillations and measure the time for 5 periods.
4. Repeat this measurement five times.
5. Repeat for 100 g, 150 g, 200 g, 250 g, and 300 g.
6. Plot T^2 versus mass.

Data:

Table I: Static determination of k:

Mass (  g  )	Fs = -W (        )	distance from unstretched position (     )
50
100
150
200
250
300

k = ______________+/- _________

Table II: Measuring the period for varous masses. You can again use the SDM Calculator. http://www2.hawaii.edu/~jmcfatri/Java/SDMCalculator.html

50 g Trial Time (5 osc.) (         ) Period (    ) 1 2 3 4 5 Tave= SD = SDM =	100 g Trial Time (5 osc.) (         ) Period (    ) 1 2 3 4 5 Tave= SD = SDM =
150 g Trial Time (5 osc.) (         ) Period (    ) 1 2 3 4 5 Tave= SD = SDM =	200 g Trial Time (5 osc.) (         ) Period (    ) 1 2 3 4 5 Tave= SD = SDM =
250 g Trial Time (5 osc.) (         ) Period (    ) 1 2 3 4 5 Tave= SD = SDM =	300 g Trial Time (5 osc.) (         ) Period (    ) 1 2 3 4 5 Tave= SD = SDM =

C = _____________
m_e = ____________

Assignments: Questions assigned: No questions to answer this section