Pendulum - Angular Amplitude with a Carbon Fiber String

1.  Attach the rotary motion sensor to the support stand.

2.  Plug the rotary motion sensor into the Pasco interface and open the template:

          K:\Physics\Demonstrations\Pendulum Motiion.cap

3.  Attach a 1-meter or 0.5-meter carbon fiber string to the rotary motion sensor and attach the mass to the "string".  The length of the pendulum is measured from the pivot point to the center of mass of the mass. The main mass is 100g and can be clamped anywhere on the "string" with the two thumbscrews.  A saddle mass of 100g can be dropped on top of the main mass to make a total mass of 200g.  A larger saddle mass of 300g can be used instead, for a total of mass of 400g.  When the saddle masses are added, the location of the center of mass does not change, so the length of the pendulum does not need to be altered.

     If the length of the pendulum is to be less than 0.50 m, the shorter carbon fiber "string" should be used.  Otherwise, the extra string length below the pendulum mass adds a large amount of air drag, causing damping of the pendulum oscillations and a increase in period over what would be predicted.

4.  With the pendulum at rest (0 degrees), click on Record, pull the pendulum up to the desired amplitude angle (measured by the digital angle meter at the upper right) and release the pendulum.

5.  After about 8-10 swings, click on Stop. Click on the graph "Highlight range of points in active data" button, and drag and resize the box around the swinging pendulum data.

The parameter ω in the curve fitting box is the circular frequency.

          Frequency   f = ω/2π  Hz

          Period        T = 2π/ω  seconds

NOTE: Both the graph and digital meter can be displayed in radians instead of degrees by selecting Rotary Motion Sensor - Angle (rad) instead of Equations/Constants - Swing (Degrees).

For small angles, the calculated valued of the period T is:

                     T ≈ 2π sqrt(L/g)

Some sample data:

     Length (m)    Amplitude (deg)    Mass (kg)    ω    T  (sec) - measured     T  (sec) - calculated   

     1.00                30                           0.100        3.11              2.02                          2.01

     1.00                10                           0.100        3.16              2.01                          2.01

     0.60                30                           0.100        3.95              1.59                          1.55

     0.60                10                           0.100        4.01              1.57                          1.55

     0.40                30                           0.100        4.87              1.29                          1.27

     0.40                10                           0.100        4.94              1.27                          1.27