Oscillations

Foreman, Dorothy              Joplin School
                              874-6161
                           

Objectives:

(1) To construct various types of pendulums.
(2) To prove that the mass of the bob and the range of the oscillation 
    (5o-15o) do not affect the period of a simple pendulum.
(3) To prove that the length of the swing arm does affect the period 
    of a simple pendulum. 
(4) To diagram each activity dealing with oscillations. 
(5) To graph length versus frequency.     
(6) To observe energy transfers in coupled pendulums of the same 
    length.
(7) To demonstrate knowledge of the formula: T=2pi times the square 
    root of L/G.
(8) To use a simple pendulum to measure the gravitational constant G.
(9) To observe the Pulfrich Pendulum and to make predictions regarding 
    the illusions it causes the eyes to see. 
(10) To use a pendulum bob to make Lissajous figures. 

Apparatus needed: 

protractors, graph paper, meter sticks, metric rulers, stop watches, 
various sizes of dowel rods, string, washers, metal balls, scissors, 
empty 2 liter plastic bottle, overhead projector, sand, balance, ring 
stands, metal supporting rods, c-clamps, scientific calculators, tape, 
polarizing film, eye hooks, wood glue, drill, saw, sand paper, screws, 
nails, wooden blocks, safety glasses. 

Recommended Strategy: 

Procedure for Pulfrich Pendulum: 
Set a simple pendulum swinging in a plane.  Have students observe its 
back and forth movement.  Have students cover one eye with polarizing 
film and observe the movement of the pendulum with both eyes open.  The 
pendulum appears to swing in a circle either clockwise or counter 
clockwise, depending upon which eye is covered.  Make predictions 
regarding the illusions.  

Procedures for testing variables: 
length, mass, and amplitude: Students will work in groups.  Set up work 
stations around the room.  Give each group washers of equal sizes, stop 
watches, protractors, c-clamps, rods, tape, string, and graph paper. 

Testing variable length: 
(1) attach one washer to each swing arm, (2) release each bob at 10 
degrees amplitude, (3) vary lengths of swing arms: 25cm, 50cm, 75cm, 
100cm, 125cm, 150cm, (4) one student will count the number of cycles in 
one minute.  (One student will either time one minute, or will time ten 
cycles)  Do three trials.  Average data. Calculate the period for each 
pendulum.  Record all data in data table.  Graph length versus time.  
Using formula, find G for each pendulum tested. 

Testing variable mass: 
(1) keep all swing arms the same length, (2) keep all amplitudes 10 
degrees, (3) vary number of washers added to swing arms, (4) record 
results, (5) reach conclusion about the affect of mass on the period of 
the simple pendulum. Testing variable amplitude: (1) keep all swing 
arms the same length, (2) add one washer to each swing arm, (3) Vary 
the amplitude from 5 degrees to 15 degrees, (4) record results, (5) 
Reach conclusion about the affect of amplitude on the period of a 
simple pendulum. 

Procedure for coupled pendulums: 
Suspend two pendulums of same length from the same thin dowel rod 
(string could be used in place of the dowel rod); suspend this rod from 
a supporting rod.  Start with the pendulums at rest.  Start one 
pendulum swinging.  The first pendulum begins to lose amplitude while 
the second pendulum starts to swing faster and faster.  At one point 
both pendulums swing together, with the same period.  Finally, the 
first pendulum comes to rest, and all the energy is in the second 
pendulum.  (1) Predict what will happen next, (2) Observe this 
phenomenon by means of an overhead projector, (3) What caused both 
pendulums to finally come to rest? 

Procedure for making Lissajous figures:
(1) fill 1/4 of plastic bob with white sand, (2) punch small hole into 
the center of bottom of the bob and cover the hole with tape, (3) 
attach large eye hook to top of bob, (4) carefully tape the bob 
together, (5) attach a short string to the eye hook, (6) attach to the 
slip knot at the top of string, another string, which when slid through 
the knot forms a triangle 7/10's the length of the entire system; 
attach each end of the string triangle to a supporting rod, (7) adjust 
rod so that the bob hangs 3cm from the black paper covered table, (8) 
uncover hole, (9) set bob in motion, (10) observe the Lissajous figures 
made out of sand. (Experiment with colored inks, sugar, etc.)