1. Physics 2215 Minilab 5: Simple Pendulum Simple Pendulum Purpose Gain experience in analyzing relationships between variables by graphical methods.

2. Physics 2215 Minilab 5: Simple Pendulum Simple Pendulum The Pendulum L  Period (T): Time for a complete swing (from A to B and back to A again). A B For   0: T 

3. Physics 2215 Minilab 5: Simple Pendulum Simple Pendulum Finding the Relationship Between T, m, A, and L Experimentally Without prior knowledge we assume: (T is some function of A, m, and L: The measured value of T may or may not depend in some way on the amplitude of the swing, the mass on the pendulum, and the length of the pendulum.) One possible functional relationship may be: where k, x, y, z are constants to be determined experimentally.

4. Physics 2215 Minilab 5: Simple Pendulum Simple Pendulum Varying One Parameter at a Time Example: Vary the amplitude , but leave the mass of the ball and the length of the string the same. Measure T for several different amplitudes.  T 5°± 1° 1.4 s ± 0.1s 10°± 1°1.5 s ± 0.1s …. use averaging as shown in manual Make suitable graphs of the data. T 

5. Physics 2215 Minilab 5: Simple Pendulum Simple Pendulum Evaluating the Data From the theoretical relationship of the period T we anticipate: - T   z = 0.5 ? - T is independent of the mass  y = 0 ? - T may or may not depend on A (  )  x = 0 ?

6. Physics 2215 Minilab 5: Simple Pendulum Simple Pendulum Is T Independent of a Amplitude? T  If linear plot of T versus A (  ) can be fit by a horizontal line (slope=0).  x=0 and T is independent of A

7. Physics 2215 Minilab 5: Simple Pendulum Simple Pendulum Is T Proportional to a Variable? T A If linear plot of T versus A can be fit by a straight line.  x=1 (T is proportional to A)

8. Physics 2215 Minilab 5: Simple Pendulum Simple Pendulum Is T  ? TIf plot of T versus can be fit by straight line.  z=1/2 is verified T L If T versus L cannot be fit by straight line:  z is neither 1 nor 0

9. Physics 2215 Minilab 5: Simple Pendulum Simple Pendulum Getting the Uncertainties in the Slopes  Please enter error bars in your graphs.  You are allowed to use the linest(…) command in Excel to determine the slope and uncertainty in the slope of the linear fits. (Note: The uncertainties from linest (…) will then be based on the scatter of the data, not on your error bars. That is OK as long as you have a sufficient number of data points to fit).

10. Physics 2215 Minilab 5: Simple Pendulum Simple Pendulum Hints Is it better to average the period by measuring 10 times a single period and averaging the result: Or is it better to measure the time of 10 periods and dividing the result by 10: To understand why the second method is better: Assume the uncertainty in a time measurement is Use error propagation to find out what is in the two cases. Which of the two methods gives a lower ?