Simple Harmonic Motion

 

Hooke's Law

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

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Simple Harmonic Motion from Energy Conservation

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

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  • Watch video clip from Lecture 13 (19:35 - 24:43)

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Oscillation in Circular Well I

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

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  • Watch video clip from Lecture 13 (24:43 - 32:46)

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Oscillation in Circular Well II

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

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  • Watch video clip from Lecture 13 (32:46 - 40:11)

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Shuttle on Circular Air Track

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

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  • Watch video clip from Lecture 13 (40:11 - 46:53)

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Ball in Circular Well

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

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Rolling Simple Harmonic Motion

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

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  • Watch video clip from Lecture 29 (46:47 - 49:35)

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Simple Harmonic Oscillation in a U-Tube

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

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  • Watch video clip from Lecture 30 (20:48 - 28:07)

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U-Tube Demonstration

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

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Torsional Pendulum Equation

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

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  • Watch video clip from Lecture 30 (32:25 - 38:34)

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Torsional Pendulum Demonstration

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

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  • Watch video clip from Lecture 30 (38:34 - 49:40)

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Oscillatory Motion

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

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

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Simple Harmonic Motion

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

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Harmonic Oscillator Problem Solving

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

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Distinct Masses Connected by Spring

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

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Simple Harmonic Oscillation

2-part SHO problem; calculating vmax and f.

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