Pendulum & Other Oscillations

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Video Clips

Pendulum Equation

RealVideo®
7:15 minutes (29:07 - 36:22)

Calculation of x(t) for pendulum; differential equation and independence of mass.

Instructor: Prof. Walter Lewin
Prior Knowledge: Sinusoidal Motion (10:09 of V10)

Spring and Pendulum Comparison

RealVideo®
4:27 minutes (36:22 - 40:49)

Dependence of T on L, g for pendulum; m, k for spring explained qualitatively.

Instructor: Prof. Walter Lewin
Prior Knowledge: Pendulum Equation (29:07 of V10)

Pendulum Periods

RealVideo®
8:09 minutes (40:49 - 48:58)

Demonstration that period is independent of both mass and angle θ.

Instructor: Prof. Walter Lewin
Prior Knowledge: Pendulum Equation (29:07 of V10)

Pendulum Oscillation Calculation II

RealVideo®
7:26 minutes (19:13 - 26:39)

Calculation of θmax by work-energy; phase angle and oscillation equation obtained.

Instructor: Prof. Walter Lewin
Prior Knowledge: Pendulum Oscillation I (12:09 of V18)

Rod Swinging on a Pin

RealVideo®
8:29 minutes (25:40 - 34:09)

Angular velocity and θ calculated for uniform rod swinging on a pin; proof of simple harmonic oscillation using torque.

Instructor: Prof. Walter Lewin
Prior Knowledge: Motion of Rod After Impulse (14:10 of V21)

Rod on a Pin Demonstration

RealVideo®
2:20 minutes (34:09 - 36:29)

Explicit calculation of T for rod on a pin; demonstration to verify.

Instructor: Prof. Walter Lewin
Prior Knowledge: Rod Swinging on a Pin (25:40 of V21)

Oscillating Hoop

RealVideo®
7:50 minutes (36:29 - 44:19)

Calculation of simple harmonic oscillation and period for swinging hoop; proof that it is the same as pendulum; demonstration of period.

Instructor: Prof. Walter Lewin
Prior Knowledge: Rod on a Pin Demonstration (34:09 of V21)

General Physical Pendulum

RealVideo®
4:11 minutes (0:00 - 4:11)

Period of physical pendulum calculated for arbitrary geometry.

Instructor: Prof. Walter Lewin
Prior Knowledge: Torque, Simple Harmonic Motion

Specific Physical Pendula

RealVideo®
11:45 minutes (4:11 - 15:56)

Period of a physical pendulum, for rod, hoop, disc, and bob; experiment to verify T for rod.

Instructor: Prof. Walter Lewin
Prior Knowledge: General Physical Pendulum (beginning of V30)

Comparison of Pendulum Dimensions

RealVideo®
4:52 minutes (15:56 - 20:48)

To obtain the same period, dimensions of physical pendula are compared and tested.

Instructor: Prof. Walter Lewin
Prior Knowledge: Specific Physical Pendula (4:11 of V30)

Lecture Notes

Pendulum

PDF - 1.1 MB#
Page 1 to page 5

Simple pendulum; physical pendulum, with example; center of oscillation; torsional pendulum; percussion; damped oscillations; and critical damping.

Instructor: Prof. Stanley Kowalski
Prior Knowledge: Oscillatory Motion

Pendulums

PDF#
Page 1 to page 14

Simple pendulum; physical pendulum, with example; center of oscillation; torsional pendulum; percussion; damped oscillations; and critical damping.

Instructor: Prof. Stanley Kowalski
Prior Knowledge: Oscillatory Motion

Pendulums and Rotational Energy

PDF
Page 1

Simple and physical pendulums defined, with equations for period; parallel axis theorem defined; kinetic energy of rotational motion; summary of linear and rotational dynamics.

Instructor: Dr. George Stephans
Prior Knowledge: Torque

Simple Pendulum

PDF
Page 18 to page 33

Instructors: Dr. Peter Dourmashkin, Prof. J. David Litster, Prof. David Pritchard, Prof. Bernd Surrow
Prior Knowledge: Rotational Dynamics, Simple Harmonic Motion

Experiment 8

PDF#
Page 1 to page 7

Physical pendulum experiment setup and procedure.

Instructors: Dr. Peter Dourmashkin, Prof. J. David Litster, Prof. David Pritchard, Prof. Bernd Surrow
Prior Knowledge: Simple Pendulum

Practice Problems

Pendulums and Collisions

PDF
Problem 29

Elastic and inelastic collisions between a pendulum bob and an object.

Instructors: Dr. Peter Dourmashkin, Prof. J. David Litster, Prof. David Pritchard, Prof. Bernd Surrow
Prior Knowledge: None

Simple Pendulum

PDF
Problem 31

Motion of a simple pendulum.

Instructors: Dr. Peter Dourmashkin, Prof. J. David Litster, Prof. David Pritchard, Prof. Bernd Surrow
Prior Knowledge: None

Ballistic Pendulum

PDF
Problem 4

Measuring the speed of a bullet by shooting a block suspended by two cables.

Instructors: Dr. Peter Dourmashkin, Prof. J. David Litster, Prof. David Pritchard, Prof. Bernd Surrow
Prior Knowledge: None

Experiment 8 Pre-Lab

PDF
Problem 5

Oscillation of a ruler suspended from one end.

Instructors: Dr. Peter Dourmashkin, Prof. J. David Litster, Prof. David Pritchard, Prof. Bernd Surrow
Prior Knowledge: None

Experiment 8 Analysis

PDF
Problem 2

Analysis of data collected in Experiment 8.

Instructors: Dr. Peter Dourmashkin, Prof. J. David Litster, Prof. David Pritchard, Prof. Bernd Surrow
Prior Knowledge: None

Pendulum I

PDF#
Problem 8

3-part pendulum problem; speed and kinetic energy at bottom, for two different masses.

Instructor: Prof. Walter Lewin
Prior Knowledge: None

Exam Questions

Projectile and Orbit

PDF#
Problem 4

Motion of a baseball thrown on a small moon of Saturn.

Instructor: Dr. George Stephans
Prior Knowledge: None

Inelastic Collision with a Spring

PDF#
Problem 6

For inelastic collision, finding initial and final velocities and pendulum attributes.

Instructors: Dr. Peter Dourmashkin, Prof. Kate Scholberg
Prior Knowledge: None

Physical Pendulum

PDF
Problem 5

Motion of an oscillating physical pendulum.

Instructors: Dr. Peter Dourmashkin, Prof. J. David Litster, Prof. David Pritchard, Prof. Bernd Surrow
Prior Knowledge: None

Physical Pendulum

PDF
Problem 1a

Period of a physical pendulum.

Instructors: Dr. Peter Dourmashkin, Prof. J. David Litster, Prof. David Pritchard, Prof. Bernd Surrow
Prior Knowledge: None

Accelerating Pendulum

PDF#
Problem 2b

Finding the period of a pendulum in a moving elevator.

Instructor: Prof. Walter Lewin
Prior Knowledge: None

Inelastic Collision with Pendulum

PDF
Problem 2c to problem 2d

Calculating θmax for pendulum after an inelastic collision between a bullet and a pendulum.

Instructor: Prof. Walter Lewin
Prior Knowledge: None