# Simple Harmonic Motion

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## Video Clips

#### Hooke's Law

RealVideo®
8:49 minutes (1:20 - 10:09)

Statement of the law, with derivation of differential equation for mass on a spring.

Instructor: Prof. Walter Lewin
Prior Knowledge: F=ma (6:52 of V6)

#### Simple Harmonic Motion from Energy Conservation

RealVideo®
5:08 minutes (19:35 - 24:43)

Derivation of differential equation for SHM from conservation of energy in a spring.

Instructor: Prof. Walter Lewin
Prior Knowledge: Force and Potential Energy (7:00 of V13)

#### Oscillation in Circular Well I

RealVideo®
8:03 minutes (24:43 - 32:46)

Equation for conservation of energy for object in circular potential well; cosine approximation.

Instructor: Prof. Walter Lewin
Prior Knowledge: Conservation of Energy (17:00 of V11)

#### Oscillation in Circular Well II

RealVideo®
7:25 minutes (32:46 - 40:11)

Derivation of differential equation for circular well; proof of simple harmonic oscillation; calculation of T and ω.

Instructor: Prof. Walter Lewin
Prior Knowledge: Oscillation in Circular Well I (24:43 of V13)

#### Shuttle on Circular Air Track

RealVideo®
6:42 minutes (40:11 - 46:53)

Demonstration of simple harmonic oscillation for shuttle on large-radius air track; calculation of T.

Instructor: Prof. Walter Lewin
Prior Knowledge: Oscillation in Circular Well II (32:46 of V13)

#### Ball in Circular Well

RealVideo®
4:36 minutes (46:53 - 51:29)

Demonstration of failure of simple harmonic motion for ball in circular well; calculation of T does not agree with SHM.

Instructor: Prof. Walter Lewin
Prior Knowledge: Oscillation in Circular Well II (32:46 of V13)

#### Rolling Simple Harmonic Motion

RealVideo®
2:48 minutes (46:47 - 49:35)

Explanation of longer than expected period for ball rolling on circular track in simple harmonic motion using rotational energy.

Instructor: Prof. Walter Lewin
Prior Knowledge: Ball in Circular Well (46:53 of V13), Rotational Kinematics (beginning of V19), Simple Harmonic Motion

#### Simple Harmonic Oscillation in a U-Tube

RealVideo®
7:19 minutes (20:48 - 28:07)

Proof of SHO and calculation of period for liquid oscillating in U-tube.

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

#### U-Tube Demonstration

RealVideo®
4:18 minutes (28:07 - 32:25)

Prediction of T for liquid in U-tube; experiment to measure T; error analysis.

Instructor: Prof. Walter Lewin
Prior Knowledge: Simple Harmonic Oscillation in a U-Tube (20:48 of V30)

#### Torsional Pendulum Equation

RealVideo®
6:09 minutes (32:25 - 38:34)

Proof of simple harmonic oscillation for torsional pendulum without small-angle; interpretation of equation.

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

#### Torsional Pendulum Demonstration

RealVideo®
11:06 minutes (38:34 - 49:40)

Calculation of T for torsional pendulum; experiment to verify T for large values of θ

Instructor: Prof. Walter Lewin
Prior Knowledge: Torsional Pendulum Equation (32:25 of V30)

## Lecture Notes

#### Oscillatory Motion

PDF - 1.6 MB#
Page 1 to page 6

Definition and properties of simple harmonic motion; mass-spring systems; energy in simple harmonic motions, with examples.

Instructor: Prof. Stanley Kowalski
Prior Knowledge: Hooke's Law, Conservation of Energy, Second Derivatives

#### Oscillatory Motion

PDF - 1.6 MB#
Page 1 to page 18

Definition and properties of simple harmonic motion; mass-spring systems; energy in simple harmonic motions, with examples; table of equations for simple harmonic motion.

Instructor: Prof. Stanley Kowalski
Prior Knowledge: Hooke's Law, Conservation of Energy, Second Derivatives

#### Simple Harmonic Motion

PDF
Page 1 to page 2

Equations for simple harmonic motion; frequency and period of simple harmonic motion; velocity, acceleration, and mechanical energy in simple harmonic motion.

Instructor: Dr. George Stephans
Prior Knowledge: Springs

#### Harmonic Oscillator Problem Solving

PDF
Page 1 to page 6

Modeling the motion of a simple harmonic oscillator; gravitational field of a spherical shell of matter; gravitational force inside uniform sphere.

Instructors: Dr. Peter Dourmashkin, Prof. J. David Litster, Prof. David Pritchard, Prof. Bernd Surrow
Prior Knowledge: Lecture 16

## Practice Problem

#### Distinct Masses Connected by Spring

PDF#
Problem 7

Masses m and 3m are connected by spring; finding energy, velocity, period of oscillations.

Prior Knowledge:
Instructor: Prof. Walter Lewin
Prior Knowledge: None