17. Periodic Motion

Simple Harmonic Motion of Pendulums

Simple Pendulum - Simple Harmonic Motion Derivation using Calculus

 A wooden meter stick is suspended from one end with a frictionless peg. If the meter stick is given a small bump and allowed to oscillate as a pendulum, what is the period of motion? 

 A 20 kg child is on a swing that has chains <math display=“inline”><mrow><mn>2</mn><mo>.</mo><mrow><mn>4</mn><mo rspace="thickmathspace">&#x2062;</mo><mi mathvariant="normal" class="MathML-Unit">m</mi></mrow></mrow></math> long. At what frequency should the child’s father deliver his pushes to ensure the highest swing possible?  

When is a Pendulum in Simple Harmonic Motion?(SHM)

Simple Harmonic Motion (1 of 16): Period of a Pendulum

simple harmonic motion - the pendulum

 A 20 kg child is on a swing that has chains <math display=“inline”><mrow><mn>2</mn><mo>.</mo><mrow><mn>4</mn><mo rspace="thickmathspace">&#x2062;</mo><mi mathvariant="normal" class="MathML-Unit">m</mi></mrow></mrow></math> long. Being interested in physics, the child’s father gives a push and then watches to see what happens. He notices that the amplitude of the child’s oscillation decreases by half in 20 s. What is the value of the time constant? 

Example

8.01x - Module 15.09 - Simple harmonic motion of pendulum.

Pendulum Equations

Anderson Video - Pendulum Mechanics

Simple Harmonic Motion (2 of 16): Pendulum, Calculating Period, Frequency, Length and Gravity

Anderson Video - The Mysterious Wave Pendulum

Simple Pendulum in Harmonic Motion

 The historic first playground on Mars has just opened. A child is on a swing with chains of length <math display=“inline”><mrow><mn>2</mn><mo>.</mo><mrow><mn>3</mn><mo rspace="thickmathspace">&#x2062;</mo><mi mathvariant="normal" class="MathML-Unit">m</mi></mrow><mo>.</mo></mrow></math> If a parent pulls the child backward <math display=“inline”><mrow></mrow></math> from equilibrium, what is the child’s maximum speed? The acceleration due to gravity on Mars is <math display=“inline”><mrow><mn>3.7</mn><msup><mrow><mtext>&#x00A0;</mtext><mtext>m/s</mtext></mrow><mn>2</mn></msup></mrow></math>. 

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