The purpose of this lab is to study simple harmonic motion of a system consisting of a mass attached to a spring. You will establish the relationship between period, mass, and spring constant.
If you need the .pdf version of these instructions you can get them here.
In this lab the phenomenon of Simple Harmonic Motion will be studied for masses on springs. The physical basis of these oscillations is that the force exerted on the mass by the spring is proportional to and in the opposite direction to the displacement of the mass from equilibrium.
In this lab, you measure the spring constant k of two springs attached a glider on an airtrack and attached to the end of the track. You measure the spring constant k in Hooke’s law for the two springs combined. (The reason for mounting two springs is that these two springs are used in Part II and III of this lab.)
The force F is supplied by the weight suspended from the string (see Fig 2. above).
You suspend various weights from the string and measure the displacement of the glider from its equilibrium position define as the position when a 100 gram weight is suspended initially.
Before you start ensure your air track is level. Attach a piece of string to the glider and lay it on the pulley with a mass m of 100g suspended from the free end of the string as shown above. Record the position of your glider for the 100g weight and define this as your equilibrium position. Be sure that the string moves freely and does not scrape. Repeat with 4 other masses of 20g each for a total of four measurements. Make sure you are taking the difference between your position readings and the equilibrium position as your data. Enter the values for the additional mass , the additional displacement and the additional force into Table 1 on your worksheet. Calculate for each of the 4 sets of numbers the slopes and enter them into Table 1.
Calculate the average and its absolute error (use (max – min)/2 for the error.) and write them on your worksheet.
In this part, you measure the period T of an oscillation caused by the two springs from Part I. The period of a mass-spring system is given by
You should note when we have both springs attached as we do in our experiment the in this equation is the sum of the spring constants of each spring. This sum is what we measured in the first part of the lab.
Remove the string from the glider and measure the mass M of the glider with the scale and record it on your worksheet (neglect error in the mass M).
Attach the glider to the two springs and place the glider on the air track so that the ‘metal flag’ atop the glider is centered at the equilibrium position.
Get ready for data taking:
You are ready for data taking now.
Calculate the theoretical period using the equation (7.3).
The error in can be calculated from the the error in you estimate in Part I. From equation 7.3 and equation (1.8) of Lab 1, if we take into account only the error of the spring constant you can find that .
Use the plotting tool to plot vs , including error bars for . Write your slope and its error on your worksheet.
In this part of the lab, you observe energy conservation. You will see that the maximum potential energy in the spring at maximum displacement from equilibrium
equals the maximum kinetic energy when the glider goes through the equilibrium point.
The setup is the same as in Part II, but you use a different file to take data.
Name: | Value: | Units: | Places: | Increment: | Editable: |
---|---|---|---|---|---|
PhotogateDistance1 | your value of w | 4 | 1.0000 | ✔ |
Now we need to check if energy is conserved.
Do these values agree within error? What does this mean for conservation of mechanical energy in simple harmonic motion?