Vernier Software and Technology
Vernier Software & Technology

Pendulum Periods

Figure from experiment 17 from Advanced Physics with Vernier — Mechanics


The introductory treatment of the motion of a pendulum leaves one with the impression that the period of oscillation is independent of the mass and the amplitude, and depends only on the length of the pendulum. These relationships are generally true so long as two important conditions are met:

  1. the amplitude is small (<< 1 radian), and
  2. the mass of the system is concentrated at the end of the string.

In this experiment and the next you will examine the behavior of a pendulum in greater detail to see what occurs when these conditions are no longer true. You will examine the approximations made to simplify the analysis of the pendulum and determine when and why these approximations begin to break down. The first of these is the subject of this experiment; the second will be examined in Experiment 18.


In this experiment, you will

  • Collect angle vs. time data for a simple pendulum.
  • Determine the best-fit equation for the angle vs. time graph.
  • From an analysis of the forces acting on the pendulum bob, derive the equation describing the motion of the pendulum.
  • Relate the parameters in the best-fit equation for the angle vs. time graph to their physical counterparts in the system.
  • Determine the period of oscillation from an analysis of the angle vs. time graph.
  • Account for the deviation from constant periods when the amplitude becomes large.

Sensors and Equipment

This experiment features the following Vernier sensors and equipment.

Additional Requirements

You may also need an interface and software for data collection. What do I need for data collection?

Advanced Physics with Vernier — Mechanics

See other experiments from the lab book.

1Motion on an Incline
2Error Analysis
3Newton's First Law
4Newton's Second Law
5Newton's Third Law
6Projectile Motion
7Energy Storage and Transfer: Elastic Energy
8Energy Storage and Transfer: Kinetic Energy
9Energy Storage and Transfer: Gravitational Energy
10AImpulse and Momentum (Motion Detector)
10BImpulse and Momentum (Photogate)
11AMomentum and Collisions (Motion Detectors)
11BMomentum and Collisions (Photogates)
12ACentripetal Acceleration
12BCentripetal Acceleration
13Rotational Dynamics
14Conservation of Angular Momentum
15Simple Harmonic Motion: Mathematical Model
16Simple Harmonic Motion: Kinematics and Dynamics
17Pendulum Periods
18Physical Pendulum
19Center of Mass

Experiment 17 from Advanced Physics with Vernier — Mechanics Lab Book

<i>Advanced Physics with Vernier — Mechanics</i> book cover

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Vernier lab books include word-processing files of the student instructions, essential teacher information, suggested answers, sample data and graphs, and more.

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