Physics 2215 Minilab 5: Simple PendulumSimple Pendulum

Purpose

• Gain experience in analyzing relationships between variables by graphical methods.

Physics 2215 Minilab 5: Simple PendulumSimple Pendulum

The Pendulum

L Q

Period (T): Time for a complete swing (from Ato B and back to A again).

A B

...

2sin

64

9

2sin

4

112 42

g

LT

For Q 0:

Tg

L2

Physics 2215 Minilab 5: Simple PendulumSimple Pendulum

Finding the Relationship Between T, m, A, and LExperimentally

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.)

LmAfT ,,

One possible functional relationship may be:

where k, x, y, z are constants to be determined experimentally.

zyx LmAkT

Physics 2215 Minilab 5: Simple PendulumSimple 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 T

5°± 1° 1.4 s ± 0.1s

10°± 1° 1.5 s ± 0.1s

…. ….

use averaging asshown in manual

Make suitable graphsof the data.

T

Q

Physics 2215 Minilab 5: Simple PendulumSimple 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 (Q) x = 0 ?

L

zyx LmAkT

Physics 2215 Minilab 5: Simple PendulumSimple Pendulum

Is T Independent of a Amplitude?

zyx LmAkT

T

( )A Q

If linear plot of T versus A (Q)can be fit by a horizontal line(slope=0).

x=0 and T is independent of A

Physics 2215 Minilab 5: Simple PendulumSimple Pendulum

Is T Proportional to a Variable?

zyx LmAkT

T

A

If linear plot of T versus Acan be fit by a straight line.

x=1 (T is proportional to A)

Physics 2215 Minilab 5: Simple PendulumSimple Pendulum

Is T ?

zyx LmAkT

T If plot of T versuscan be fit by straight line. z=1/2 is verified

L

T

L

L

If T versus L cannot be fit by straight line: z is neither 1 nor 0

L

Physics 2215 Minilab 5: Simple PendulumSimple 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).

Physics 2215 Minilab 5: Simple PendulumSimple 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:

10

...10/10 1021 TTT

PeriodsofSumT

10

10 periodsofTimeT

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 ?

tT

T