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Pendula

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Prerequisites

Lab Activities

Spacer Students study the motion of a simple pendulum, a physical pendulum and a torsional pendulum and compare the observed motion with the simple harmonic motion predicted by theory for small oscillations of these systems.

Spacer The specific theoretical relationships investigated are:

a. for a simple pendulum

T^2 = 4*pi^2*l/g

where T is the period of oscillation, l is the length of the pendulum and g is the acceleration of gravity;

b. for a physical pendulum

T^2 = ((4*pi^2)/g) * ((I + ml^2)/ml)

where I is the moment of inertia, m is the mass of the pendulum and l is the distance from the pivot point to the center of mass;

c. for a torsional pendulum

T^2 = (4*pi^2)*(I/k)

where k is a constant.

Spacer Students are required to best determine how to present their data so as to confirm the theoretical expressions stated above. Standard methods of data analysis are emphasized. Quantitative results tend to be within 2% of the accepted values.

Course Level

Introductory: P3, P13, P15

Student Handouts

Equipment

Number of set-ups available: 5

Per lab station:

Simple pendula setup:

1 c-clamp
1 large bar (1" diameter - 1 meter in length)
1 medium bar (0.5' diamter - 0.5 meter in length)
1 ring stand clamp
1 ball of string
1 pair of scissors
1 200 gm, 100 gm, and 50 gm hooked masses
1 stopwatch
1 meter stick

Physical pendula setup:

1 ring stand
1 ring stand clamp
1 physical pendulum
1 short bar with knife edge
1 balance/standard mass set
1 stopwatch
1 meter stick
1 vernier caliper
1 center of mass pan/string

Torsional pendula setup:

1 ring stand
1 ring stand clamp
1 torsional pendulum
1 short bar with knife edge
1 balance/standard mass set
1 stopwatch
1 meter stick
1 vernier caliper
1 center of mass pan/string
2 large cylindrial masses
2 smaller cylindrial masses

Simple Pendulum Setup

pendulum

Physical Pendulum Setup

physical pendulum

Torsional Pendulum Setup

torsional pendulum

Notes


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