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Work done on the system is force multiplied by distance which equals the area under the curve or A in the | [
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Another way to determine the work is to note that the force increases linearly from 0 to kx so that the average force is the distance moved isx and thus B in the Chapter 16 Oscillatory Motion and Waves 685Figure 16 6 A graph of applied force versus distance for the deformation of a system that can be described by s law... | [
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The work done on the system equals the area under the graph or the area of the triangle which is half its base multiplied by its height or Example 16 2 Calculating Stored A Tranquilizer Gun Spring We can use a toy spring mechanism to ask and answer two simple How much energy is stored in the spring of a tranquilizer gu... | [
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The expression for kinetic energy can be solved for the speed Solution for b686 Chapter 16 Oscillatory Motion and Waves This OpenStax book is available for free at 141 | [
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Identify known PEelor 0 563 J 2 | [
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Solve for 563 0 002 23 3 | [
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Convert 23 7 Discussion and This projectile speed is impressive for a tranquilizer gun than 80 | [
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The numbers in this problem seem reasonable | [
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The force needed to compress the spring is small enough for an adult to manage and the energy imparted to the dart is small enough to limit the damage it might do | [
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Y et the speed of the dart is great enough for it to travel an acceptable distance Check your Understanding Envision holding the end of a ruler with one hand and deforming it with the other | [
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When you let go you can see the oscillations of the ruler | [
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In what way could you modify this simple experiment to increase the rigidity of the Solution You could hold the ruler at its midpoint so that the part of the ruler that oscillates is half as long as in the original experiment Check your Understanding If you apply a deforming force on an object and let it come to equili... | [
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Each successive vibration of the string takes the same time as the previous one | [
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We define periodic motion to be a motion that repeats itself at regular time intervals such as exhibited by the guitar string or by an object on a spring moving up and down | [
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The time to complete one oscillation remains constant and is called the periodT | [
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Its units are usually seconds but may be any convenient unit of time The word period refers to the time for some event whether repetitive or but we shall be primarily interested in periodic motion which is by definition repetitive | [
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A concept closely related to period is the frequency of an event | [
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For example if you get a paycheck twice a month the frequency of payment is two per month and the period between checks is half a month | [
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Frequency fis defined to be the number of events per unit time | [
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For periodic motion frequency is the number of oscillations per unit time The relationship between frequency and period is T The SI unit for frequency is the cycle per second which is defined to be a hertz Hz 1cycle secor 1 Hz A cycle is one complete oscillation | [
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Note that a vibration can be a single or multiple event whereas oscillations are usually repetitive for a significant number of cycles Example 16 3 Determine the Frequency of Two Medical Ultrasound and the Period of Middle C We can use the formulas presented in this module to determine both the frequency based on known... | [
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try one example of each A medical imaging device produces ultrasound by oscillating with a period of 0 400 | [
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What is the frequency of this The frequency of middle C on a typical musical instrument is 264 Hz | [
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