PHYS 205

SPR 2007

The Simple Pendulum

Materials:light string, meter stick, stopwatch, various masses

  • Your simple pendulum will consist of a mass suspended by light thread from a point about which it can freely swing.
  • The displacement of the pendulum will be the angle at which it is pulled back before release to swing.
  • Thelength is the distance from the point of suspension to the center of gravity of the mass.
  • You will measure the period (the time it takes for the pendulum bob to swing from one side to the other and back again) while individually varying the mass, length, and angular displacement of the pendulum.

I. Does mass affect the period of a pendulum?

A.Use a length of string between 0.60 m and 1.20 m. Tie a mass to the string. Pull the pendulum bob back about 30 and record the time it takes for the pendulum to make 10 complete cycles. Divide this time by 10 to get the period of the pendulum.

b. Record this information in DATA TABLE I.

c. Now perform the same procedure, but use a different mass. Be sure to keep all other variables EXACTLY the same as before.

d. Repeat these steps for the other masses. Record all information in the data table.

II. DOES LENGTH AFFECT THE PERIOD OF A PENDULUM?

  1. Find the period of the pendulum as you did above, but use the same mass and amplitudein each trial, while varying only the pendulum’slength.
  2. Do this according to DATA TABLE II.

III. DOES AMPLITUDE AFFECT THE PERIOD OF A PENDULUM?

  1. This time use a constant length and mass, but vary the amplitude (angle) through which the pendulum swings.
  2. Find the period of the pendulum with initial amplitudes given in DATA TABLE III.
  3. Record all information in the data table.

Useyour results and the formula for the approximate period of a pendulum to calculate the acceleration of gravity for each trial.

DATA TABLE I – Variable Mass

Mass,
g / Length,
m / Amplitude,
deg / Time, s
10 cycles / Period,
s / g,
m/s2
20
50
100
200
500

DATA TABLE II – Variable Length

Mass,
g / Length,
m / Amplitude,
deg / Time, s
10 cycles / Period,
s / g,
m/s2
0.20 m
0.35 m
0.50 m
0.65 m
0.80 m
0.95 m
1.10 m
1.25 m
1.40 m

DATA TABLE III – Variable Amplitude

Mass,
g / Length,
m / Amplitude,
deg / Time, s
10 cycles / Period,
s / g,
m/s2
10
20
30
40
50

Results:

Make a graph of “Period vs Mass” using the results of Data Table I.

Make a graph of “Period vs Length” using the results from Data Table II.

Make a graph of “Period vs Amplitude” using the results of Data Table III.

Scale each graph appropriately in order to best present the relationship between the variables.

On each graph, write a statement commenting on the relationship between the period and the manipulated variable that is indicated by the shapes of the graphs. For example, you may find relationships that are directly proportional, inversely proportional, quadratic, square root, sinusoidal, or you may find no relationship at all.

Write a summary paragraph describing what you learned about pendulums from this activity.

Period of a Mass on a Spring

Objective:

To investigate the period of oscillation of a mass and spring system.

Materials: Hooke’s Law apparatus, stopwatch, various masses

Procedure:

  • Place mass on the spring according to values specified in the

DataTable.

  • Gently lift the mass 2 or 3 cm.
  • Start the stopwatch when the mass is released and time 10

completevibrations.

  • Record the total time for 10 complete vibrations in the Data Table.
  • Divide this total time by 10 in order to determine the period ofvibration.
  • Continue this process until the Data Table is complete.
  • State a generalization regarding how mass affects the period of an oscillating spring.

Data Analysis:

  • Make a graph of “Period vs Mass” using results from the Data Table. Be sure to include the origin as one of your data points.
  • Describe the shape of this graph.
  • Based on the shape of your graph, state the relationship between the period of an oscillating spring and the amount of mass placed on that spring.
  • If possible, use MS Excel or your graphing calculator to obtain the best-fit equation of your graph. Record this equation on the graph.
  • List sources of error in this investigation.

DATA TABLE

Hanging Mass,
g / Total Time,
s / Complete Oscillations / Period,
s
100 / 10
200 / 10
300 / 10
400 / 10
500 / 10
600 / 10
700 / 10
800 / 10

Extension:

Compare this activity to the Inertial Balance activity.

Could this procedure be used to accurately determine an unknown mass…

…in the lab?

…on the moon?

…in outer space (no gravity)?

Be sure to explain your answers.

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