Physics 2215 Minilab 5 Simple Pendulum Purpose Gain

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

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

Physics 2215 Minilab 5: 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.

Simple Pendulum Physics 2215 Minilab 5: Simple Pendulum Varying One Parameter at a Time Example: Vary the amplitude Q, but leave the mass of the ball and the length of the string the same. Measure T for several different amplitudes. A (Q) 5°± 1° T use averaging as shown in manual 1. 4 s ± 0. 1 s 10°± 1° 1. 5 s ± 0. 1 s …. T …. Make suitable graphs of the data. Q

Physics 2215 Minilab 5: Simple Pendulum Evaluating the Data • From 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 (Q) x = 0 ?

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

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

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

Physics 2215 Minilab 5: Simple Pendulum Getting the Uncertainties in the Slopes Ø Please enter error bars in your graphs. Ø 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).

Physics 2215 Minilab 5: 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 ?