17. Periodic Motion

Simple Harmonic Motion of Pendulums

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

You pull a simple pendulum 0.240 m long to the side through an angle of 3.50° and release it. (a) How much time does it take the pendulum bob to reach its highest speed?

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?

Simple Pendulum - Simple Harmonic Motion Derivation using Calculus

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

You pull a simple pendulum 0.240 m long to the side through an angle of 3.50° and release it. (b) How much time does it take if the pendulum is released at an angle of 1.75° instead of 3.50°?

A certain simple pendulum has a period on the earth of 1.60 s. What is its period on the surface of Mars, where g = 3.71 m/s^2?

A building in San Francisco has light fixtures consisting of small 2.35-kg bulbs with shades hanging from the ceiling at the end of light, thin cords 1.50 m long. If a minor earthquake occurs, how many swings per second will these fixtures make?

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

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

A simple pendulum 2.00 m long swings through a maximum angle of 30.0° with the vertical. Calculate its period (a) assuming a small amplitude, and (b) using the first three terms of Eq. (14.35). (c) Which of the answers in parts (a) and (b) is more accurate? What is the percentage error of the less accurate answer compared with the more accurate one?

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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