PHY-104 Lecture Chapter 11 Part 2
1. Intro
a. Problems?
i. Text Problems?
ii. Pick up Chapters 11 &12 up front
iii. Mastering Physics Problems?
b. Collect Problem 11.67 and distribute solutions
c. New Mastering Physics Assignment posted
i. Chapter 11 Problems 26, 27, 30, 32, 34, 40, 41, 47, 48, 54, 61, 63
ii. Mastering Physics says that this assignment should take 127 minutes
d. Hand in on Tuesday the following Problem 11:60
2. Lab Write up Instructions – Review in class
3. Periodic Motion
a. Demonstrate and define the following terms
i. Amplitude of the Motion, A
ii. A Cycle of the Motion
iii. The Period of the Motion, T
1. Units are seconds per cycle, s
iv. The Frequency of the Motion, f
1. Units in Cycles/seconds or Hertz
2.
f 
1
T
v. The Angular Frequency of the Motion, 
1. Units in radians/second or s-1
2.   2f 
2
T
b. For a periodic motion to be simple harmonic motion there must be a restoring force that
is directly proportional to the displacement from equilibrium


FRestoring  k  x
Why the negative sign? The restoring force must be in the opposite direction to the
displacement.
Consider the situation we are demonstrating. See 11.14 in text. Use hand written notes.
Conclusion: The net force on the cart is restoring and proportional to the displacement
from equilibrium. Therefore the motion is simple harmonic motion.
Not all periodic motion is SHM motion. However, many complex systems will oscillate
simple harmonically when the amplitude of the oscillation is small. This concept has
applications over an incredibly large range of length scales; from vibrating atoms to
pulsating stars.
Remember, even when there is no physical spring involved, the effective “spring
constant” can be constructed using the appropriate elastic modulus (Young’s Y, Bulk B
or Shear S) and the physical dimensions of the particular application.
c. Example 11.4
4. Energy in Simple Harmonic Motion Equations of Simple Harmonic Motion
a. See Hand written notes
b. Quantitative Analysis 11.1 pg. 344
c. Example 11.5
5. Equations of Simple Harmonic Motion
a. The Reference Circle
i. Draw the reference circle with a particle moving around is circumference a t
constant speed v0 and v0 
2  A
 2f  A    A
T
ii. Find the particles x-position at some point Q on the circle
1. Draw 11.20 b
2. x  A cos  and     t (i.e. constant angular frequency)
iii. Find the particles x-velocity at some point Q
1. Draw 11.21 a
2. v x  v0 sin   A sin 
iv. Find the particles x-acceleration at some point Q
1. Draw 11.21 b
2. The acceleration is directed toward the center with magnitude
v02
A
3. The x-component of that acceleration is
 v02
  2 A2
 cos  
 cos    2 A  cos 
A
A
2
2
v. Finally we get to an interesting point a x   A  cos     x . Since the xax 
acceleration at any instant is a x   2  x , then the motion in the x-direction is
simply harmonic. And the equations we derived for the x components of
position, velocity and acceleration on the unit circle can be applied to ALL
particles in SHM.
b. Thus, for any object in SHM the following equations will apply (with appropriate
symbol; changes to suit the problem)
i.     t
2
T
iii. x  A cost 
iv. v  Asin t 
2
v. a x   A  cost 
ii.   2f 
c. Quantitative Analysis 11.2 on page 348
d. Quantitative Analysis 11.3 on page 349
e. Example 11.6
f. Example 11.7
6. The Simple Pendulum
a. Examine the motion of a Simple Pendulum. See handwritten notes
b. Example 11.8
7. Resonance
a. Demo
b. Tacoma Narrow video
c. Russian Bridge