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<title>ReadingGuide_Ch15_Solution</title>
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<h1>Chapter 15 – Oscillations</h1>
<h3>Introduction</h3>
<p>- Why does a 300,000 gallon tank sit on top of the Comcast Building in
Philadelphia? <span id="ans">To reduce oscillations.</span></p>
<p></p>
<h3>15.1 – Simple Harmonic Motion</h3>
<p>- What is periodic motion? <span id="ans">Any motion that repeats itself at
regular intervals. </span></p>
<p>- What is period? frequency? How do they relate? <span id="ans">Period -
time it takes to do 1 oscillation. Frequency - number of oscillations per unit
time. Equation 15.1. </span></p>
<p>- What is the SI unit of frequency? What other base units is it equivalent
to? <span id="ans">Hertz. 1Hz = 1/s. </span></p>
<p>- What is simple harmonic motion? <span id="ans">The net force of the system
is proportional to the displacement and acts in the opposite direction of the
displacement. </span></p>
<p>- What is amplitude? <span id="ans">Maximum displacement from
equilibrium.</span> </p>
<p>- What is equilibrium position? What is the net force at the equilibrium
position? <span id="ans">Position where a spring is neither stretched nor
compressed. The net force is zero.</span></p>
<p>- What is the equation for the position as a function of time for simple
harmonic motion? See Figure 15.4 and 15.5 to see how to apply it. <span
id="ans">Equation 15.2.</span> </p>
<p>- What is a phase shift? <span id="ans">Angle, in radians, that is used in a
cosine or sine function to shift the function left or right, used to match up
the function with the initial conditions of the data. </span></p>
<p>- Understand how to obtain the velocity and acceleration vs time for from
the position function. </p>
<p>- Know equations 15.3-15.8. Example 15.2 (Determining the Equations of
Motion for a Block and a Spring) shows how to use them.</p>
<p>- What are the equations for angular frequency, period, and frequency for a
mass on a spring? <span id="ans1">Equations 15.9, 15.10, 15.11.</span></p>
<p>- Understand Figure 15.10. It helps visualize the position, velocity, and
acceleration of a mass hanging from a spring.</p>
<h3>15.2 – Energy in Simple Harmonic Motion</h3>
<p>- What is the potential energy of a spring? <span id="ans">Equation in the
middle of pdf page 760.</span></p>
<p>- What is the total energy of a block and spring system? <span
id="ans">Equation at the top of pdf page 762. </span></p>
<p>- The energy oscillations of a block and spring system can be seen in Figure
15.12. What type of energy is constant in simple harmonic motion, Kinetic,
Potential, or Total?<span id="ans">Total.</span> </p>
<p>- What equation is the velocity of a simple harmonic oscillator for any
position? <span id="ans">Equation 15.13.</span></p>
<h3>15.3 – Comparing Simple Harmonic Motion and Circular Motion</h3>
<p>- Understand the arguments in Figure 15.18 and how to obtain Equations 15.14
- 15.16. Notice that they are similar to Equations 15.3 - 15.5.</p>
<h3>15.4 – Pendulums</h3>
<p>- What is a simple pendulum? <span id="ans">A point mas (pendulum bob)
suspended from a string with negligible mass.</span></p>
<p>- What are the equations for angular frequency and period for simple
pendulum? <span id="ans">Equations 15.17, 15.18, 15.19.</span></p>
<p>- Check the small angle approximation using your calculator. For small
angles (<15 degrees), sin theta ~ theta, when theta is measured in radians.
</p>
<p>- Example 15.2 (Measuring Acceleration due to Gravity by the Period of a
Pendulum) shows you can use a pendulum to measure g. </p>
<p>- What is a physical pendulum? How is it different from a simple pendulum?
<span id="ans">Any object that oscillates like a simple pendulum, but cannot be
modelled as a point mass on a string.</span></p>
<p>- What are the equations for angular frequency and period for a physical
pendulum? <span id="ans">Equations 15.20, 15.21.</span></p>
<p>- What is torsional pendulum? <span id="ans">Rigid body suspended a light
wire or spring. When it is twisted, the body oscillates.</span> </p>
<p>- What is the equation for period for a torsional pendulum? What is kappa?
What are its units? <span id="ans">Equation 15.22. Kappa is a torsion constant,
has units of kg*m^2/s^2. </span></p>
<h3>15.5 - Damped Oscillations</h3>
<p>- What is a damped oscillation? <span id="ans">An oscillation with friction
present.</span></p>
<p>- What is the differential equation for damped oscilltions? What is its'
solution? <span id="ans">Equation 15.23. Equation 15.24. </span></p>
<p>- What is the equation for the natural angular frequency? <span
id="ans">Equation 15.25. </span></p>
<p>- What is the equation for angular frequency of damped oscillations? <span
id="ans">Equation 15.26. </span></p>
<p>- What does underdamped, critically damped, and underdamped oscillations
mean? <span id="ans">Underdamped - oscillations die off exponentially,b^2 <
4mk. Critically damped - b^2=4mk. Overdamped - b^2 > 4mk, takes longest to
get to equilibrium. </span></p>
<h3>15.6 - Forced Oscillations </h3>
<p>- What is a forced oscillation? <span id="ans">A system that is forced to
oscillate. </span></p>
<p>- What is resonance? <span id="ans">When a system is driven at its natural
frequency.</span></p>
<p>- What is the differential equation for forced oscillations? What is its'
solution? <span id="ans">Equation 15.27. Equation 15.28.</span></p>
<p>- What is its amplitude? <span id="ans">Equation 15.29. </span></p>
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