chapter14

Chapter 14 SIMPLE HARMONIC MOTION blaahblaaah aaaaaaaaa

[] toc = = hello  Welcome physics scholars! Undoubtedly, you are here to uncover the wonders of oscillation and Simple Harmonic Motion. You will soon discover that with the knowledge of a few relatively simple equations and mastery of some basic concepts, you will find very little trouble solving a variety of oscillation-based problems. Here you will find information on the topics covered in Chapter 14, followed by practice problems (both multiple choice and free response), an online interactive lab, a discussion of real-world applications, and links to more Simple Harmonic Motion fun. Happy learning! = = = = =Oscillation/Springs =

Motion




Spring Constant
= Spring Concepts Chart = **SPRING CONCEPTS CHART **
 * The unit for **k** is N/m

= Pendulums =

= Physical Pendulums =

= Damped Harmonic Motion =



= Practice Problems =

Multiple Choice Problems


**5. Which graph has the highest Q factor? ** **A. **    
 * B. **
 * C. **
 * ﻿D. **

Free Response Problems










Problem Solutions






=<span style="font-family: 'Times New Roman',Times,serif;">﻿Laboratory = = = <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">**Pendulum Applet Lab** <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">Adapted from a lab by Geoff Phillips ([])

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">Go to the Pendulum Applet at the following URL:

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">[]

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">Run the ‘**Pendulum lab’ java simulation** with a 1 kg single pendulum and use it to investigate the relationship between the pendulum’s period (//T//) and the independent variable ‘length’ (//L//).

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">**Part A** <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">Vary length (keep angle fixed at 30°)
 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">Length (L) || asaadfgh || asaadfgh || aaasdfgh || asdaafgh || asdfgaah || asaadfgh || asaadfgh || asdfaagh || asdfghaa ||
 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">Period (T) ||  ||   ||   ||   ||   ||   ||   ||   ||   ||

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">**Part B** <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">Use a spreadsheet and a **Power fit** trendline to produce graph of T vs. L. Display the equation on your graph.

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">**Part C** <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">Use this equation to test to see if the applet’s estimation of //g// (acceleration due to gravity) is accurate (approximately 9.8). <span style="font-family: 'Times New Roman',Times,serif; font-size: 15px;">[Hint: the exponent should be roughly 0.5, so estimate it as such]

Sample Results
==

=<span style="color: black; font-family: 'Times New Roman',Times,serif;">Real World Applications =

<span style="font-family: Arial,Helvetica,sans-serif;">Courtesy of <span style="color: black; font-family: Arial,Helvetica,sans-serif;">[]

<span style="color: black; font-family: Arial,Helvetica,sans-serif;">Springs
<span style="color: black; font-family: Arial,Helvetica,sans-serif;">“Springs are a major part of everyday life. They can be found in everything from the shock-absorber assembly of a motor vehicle to the supports of a trampoline fabric, and in both cases, springs blunt the force of impact.

<span style="color: black; font-family: Arial,Helvetica,sans-serif;">If one were to jump on a piece of trampoline fabric stretched across an ordinary table—one with no springs—the experience would not be much fun, because there would be little bounce. On the other hand, the elastic potential energy of the trampoline's springs ensures that anyone of normal weight who jumps on the trampoline is liable to bounce some distance into the air. As a person's body comes down onto the trampoline fabric, this stretches the fabric (itself highly elastic) and, hence, the springs. Pulled from a position of equilibrium, the springs acquire elastic potential energy, and this energy makes possible the upward bounce.

<span style="color: black; font-family: Arial,Helvetica,sans-serif;">As a car goes over a bump, the spring in its shock-absorber assembly is compressed, but the elastic potential energy of the spring immediately forces it back to a position of equilibrium, thus ensuring that the bump is not felt throughout the entire vehicle. However, springs alone would make for a bouncy ride; hence, a modern vehicle also has shock absorbers. The shock absorber, a cylinder in which a piston pushes down on a quantity of oil, acts as a damper—that is, an inhibitor of the springs' oscillation.”

<span style="color: black; font-family: Arial,Helvetica,sans-serif;">Elasticity
<span style="color: black; font-family: Arial,Helvetica,sans-serif;">“Many objects in daily life oscillate in a spring-like way, yet people do not commonly associate them with springs. For example, a rubber band, which behaves very much like a spring, possesses high elastic potential energy. It will oscillate when stretched from a position of stable equilibrium. <span style="color: black; font-family: Arial,Helvetica,sans-serif;">Rubber is composed of long, thin molecules called polymers, which are arranged side by side. The chemical bonds between the atoms in a polymer are flexible and tend to rotate, producing kinks and loops along the length of the molecule. The super-elastic polymers in rubber are called elastomers, and when a piece of rubber is pulled, the kinks and loops in the elastomers straighten.

<span style="color: black; font-family: Arial,Helvetica,sans-serif;">The structure of rubber gives it a high degree of elastic potential energy, and in order to stretch rubber to maximum displacement, there is a powerful restoring force that must be overcome. This can be illustrated if a rubber band is attached to a ceiling, like the spring in the earlier example, and allowed to hang downward. If it is pulled down and released, it will behave much as the spring did.

<span style="color: black; font-family: Arial,Helvetica,sans-serif;">The oscillation of a rubber band will be even more appreciable if a weight is attached to the "free" end—that is, the end hanging downward. This is equivalent, on a small scale, to a bungee jumper attached to a cord. The type of cord used for bungee jumping is highly elastic; otherwise, the sport would be even more dangerous than it already is. Because of the cord's elasticity, when the bungee jumper "reaches the end of his rope," he bounces back up. At a certain point, he begins to fall again, then bounces back up, and so on, oscillating until he reaches the point of stable equilibrium.”

<span style="color: black; font-family: Arial,Helvetica,sans-serif;">Pendulums
<span style="color: black; font-family: Arial,Helvetica,sans-serif;">“As noted earlier, a pendulum operates in much the same way as a swing; the difference between them is primarily one of purpose. A swing exists to give pleasure to a child, or a certain bittersweet pleasure to an adult reliving a childhood experience. A pendulum, on the other hand, is not for play; it performs the function of providing a reading, or measurement.

<span style="color: black; font-family: Arial,Helvetica,sans-serif;">One type of pendulum is a metronome, which registers the tempo or speed of music. Housed in a hollow box shaped like a pyramid, a metronome consists of a pendulum attached to a sliding weight, with a fixed weight attached to the bottom end of the pendulum. It includes a number scale indicating the number of oscillations per minute, and by moving the upper weight, one can change the beat to be indicated.

<span style="color: black; font-family: Arial,Helvetica,sans-serif;">Metronomes were developed in the early nineteenth century, but, by then, the concept of a pendulum was already old. In the second century A.D., Chinese mathematician and astronomer Zhang Heng (78-139) used a pendulum to develop the world's first seismoscope, an instrument for measuring motion on Earth's surface as a result of earthquakes.

<span style="color: black; font-family: Arial,Helvetica,sans-serif;">Zhang Heng's seismoscope, which he unveiled in 132 A.D., consisted of a cylinder surrounded by bronze dragons with frogs (also made of bronze) beneath. When the earth shook, a ball would drop from a dragon's mouth into that of a frog, making a noise. The number of balls released, and the direction in which they fell, indicated the magnitude and location of the seismic disruption.”

<span style="font-family: Arial,Helvetica,sans-serif;">“In 718 A.D., during a period of intellectual flowering that attended the early T'ang Dynasty (618-907), a Buddhist monk named I-hsing and a military engineer named Liang Ling-tsan built an astronomical clock using a pendulum. Many clocks today—for example, the stately and imposing "grandfather clock" found in some homes—like-wise, use a pendulum to mark time.

<span style="color: black; font-family: Arial,Helvetica,sans-serif;">Physicists of the early modern era used pendula (the plural of pendulum) for a number of interesting purposes, including calculations regarding gravitational force. Experiments with pendula by Galileo Galilei (1564-1642) led to the creation of the mechanical pendulum clock—the grandfather clock, that is—by distinguished Dutch physicist and astronomer Christiaan Huygens (1629-1695).

<span style="color: black; font-family: Arial,Helvetica,sans-serif;">In the nineteenth century, A Scottish inventor named Alexander Bain (1810-1877) even used a pendulum to create the first "fax machine." Using matching pendulum transmitters and receivers that sent and received electrical impulses, he created a crude device that, at the time, seemed to have little practical purpose. In fact, Bain's "fax machine," invented in 1840, was more than a century ahead of its time.”

[]

=<span style="color: black; font-family: 'Times New Roman',Times,serif; font-size: 120%;">Links =

**<span style="color: black; font-family: 'Times New Roman',Times,serif;">Spring Applet ** []

**<span style="font-family: 'Times New Roman',Times,serif;">Simple Harmonic Motion Applets ** []

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">**Pendulum Applet** <span style="font-family: Arial,Helvetica,sans-serif; font-size: 110%;">[]






 * CATEGORY ||  SCORE (1-4)  ||  POINTS (0-20)  ||
 * Content || 4 || 20 ||
 * Organization || 4 || 20 ||
 * Accuracy || 4 || 20 ||
 * Appearance || 4 || 20 ||
 * Participation || 4 || 20 ||
 * TOTAL || 100 ||
 * TOTAL || 100 ||