17. Periodic Motion

Intro to Simple Harmonic Motion (Horizontal Springs)

Energy in Horizontal Springs Example

Anderson Video - Period of an Oscillating Spring

Anderson Video - Cosine Solution to Simple Harmonic Motion

Anderson Video - Spring Example- Max Speed and Acceleration

Example

A 4-kg mass on a spring is released 5 m away from equilibrium position and takes 1.5 s to reach its equilibrium position. (a) Find the spring’s force constant. (b) Find the object’s max speed.

A certain astronaut oscillates back and forth on a chair attached to springs. The spring constants are such that when her mass is known to be <math display=“inline”><mrow><mn>55</mn><mo>.</mo><mrow><mn>0</mn><mo rspace="thickmathspace">&#x2062;</mo><mi mathvariant="normal" class="MathML-Unit">kg</mi></mrow><mo>,</mo></mrow></math> she oscillates with a period of <math display=“inline”><mrow><mn>2</mn><mo>.</mo><mrow><mn>85</mn><mo rspace="thickmathspace">&#x2062;</mo><mi mathvariant="normal" class="MathML-Unit">s</mi></mrow><mo>.</mo></mrow></math> After some time in space, a repetition of the measurement yields a period of <math display=“inline”><mrow><mn>2</mn><mo>.</mo><mrow><mn>75</mn><mo rspace="thickmathspace">&#x2062;</mo><mi mathvariant="normal" class="MathML-Unit">s</mi></mrow><mo>.</mo></mrow></math> What is the astronaut’s mass now?

A 250 g air-track glider attached to a spring oscillates with maximum speed of <math display=“inline”><mrow><mn>0</mn><mo>.</mo><mn>97</mn><mo rspace="thickmathspace">&#x2062;</mo><mrow><mfrac bevelled="true"><mi mathvariant="normal" class="MathML-Unit">m</mi><mi mathvariant="normal" class="MathML-Unit">s</mi></mfrac></mrow></mrow></math>. If the spring has a spring constant of <math display=“inline”><mrow><mn>450</mn><mo rspace="thickmathspace">&#x2062;</mo><mrow><mfrac bevelled="true"><mi mathvariant="normal" class="MathML-Unit">N</mi><mi mathvariant="normal" class="MathML-Unit">m</mi></mfrac></mrow></mrow></math>, at what distance from the equilibrium position will the glider have a speed of <math display=“inline”><mrow><mn>0</mn><mo>.</mo><mn>43</mn><mo rspace="thickmathspace">&#x2062;</mo><mrow><mfrac bevelled="true"><mi mathvariant="normal" class="MathML-Unit">m</mi><mi mathvariant="normal" class="MathML-Unit">s</mi></mfrac></mrow></mrow></math>?

Anderson Video - Simple Harmonic Motion

Anderson Video - Graphing Simple Harmonic Motion and Determining Phi

How To Solve Simple Harmonic Motion Problems In Physics

Simple Harmonic Motion Derivations using Calculus (Mass-Spring System)

Simple Harmonic Motion: Crash Course Physics #16

Anderson Video - Speed of a Block on a Spring

What is the equation for the position of a mass moving on the end of a spring which is stretched 8.8cm from equilibrium and then released from rest, and whose period is 0.66s? What will be the object’s position after 1.4s?

A mass-spring system with an angular frequency ω = 8π rad/s oscillates back and forth. (a) Assuming it starts from rest, how much time passes before the mass has a speed of 0 again? (b) How many full cycles does the system complete in 60s?

Physics - Mechanics: Ch 16.5 Simple Harmonic Motion-2 Springs (1 of 5) 2 Equal Springs, 1 Mass

 An air-track glider attached to a spring oscillates between the 50 cm mark and the 62 cm mark. It completes seven oscillations in 10 s. What is the maximum speed of the glider as it oscillates? 

Equations of Simple Harmonic Motion

Simple Harmonic Motion 2 - Mass on a horizontal spring

Intro to Simple Harmonic Motion

Simple Harmonic Motion Introduction(SHM) via a Horizontal Mass-Spring System

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