Lesson 1-Vibrations

1. Lesson 1 - Vibrations
 Introduction to WavesIntroduction to Waves
Nelson Reference Pages:Nelson Reference Pages:
378, 381-382, 385-387, 430-431

2. Amplitude, Period, & Frequency
 A pendulum swings back and forth with each cycle, orA pendulum swings back and forth with each cycle, or
vibration, taking an equal amount of time. The amount ofvibration, taking an equal amount of time. The amount of
time (in “s”) for 1 cycle is called ______ ( ). If we calculatetime (in “s”) for 1 cycle is called ______ ( ). If we calculate
the reciprocal of this quantity, we get the number of cyclesthe reciprocal of this quantity, we get the number of cycles
per second. This quantity is called the __________ and isper second. This quantity is called the __________ and is
measured inmeasured in hertz (Hz). TheThe ⊥⊥ distance from the pendulumdistance from the pendulum
bobbob to its equilibrium position, is called _________ ( ) .to its equilibrium position, is called _________ ( ) .
U p
B o b B o b
A A
B o b
a
b
c
A
A T IM E
a
b b
c
a
O n e C y c le
T

3.  TheThe amplitude vs. time graph should look like agraph should look like a
cosine function. All graphs that represent acosine function. All graphs that represent a
sine, or cosine, function are calledsine, or cosine, function are called sinusoidal.
 If the motion of the bob isIf the motion of the bob is ⊥⊥ to its length we callto its length we call
thisthis transverse vibration. If the motion of theIf the motion of the
object, or bob, is // to its length, we call thisobject, or bob, is // to its length, we call this
longitudinal vibration. A mass attached to theA mass attached to the
end of a vertical spring, and moving up & down,end of a vertical spring, and moving up & down,
would have this type of vibration.would have this type of vibration.
 http://www.youtube.com/watch?v=eeYRkW8V7Vghttp://www.youtube.com/watch?v=eeYRkW8V7Vg
 http://www.youtube.com/watch?v=U3K_zGT9STohttp://www.youtube.com/watch?v=U3K_zGT9STo

4.  Q.Q. How does
amplitude affect the
period of vibration?
 In the diagram:In the diagram:
A1,, A2 are theare the
amplitudes andamplitudes and a, b
& c indicate theindicate the
position of the bobposition of the bob
during its swing,during its swing,
((b is the rest
position).).
 A.A. Amplitude does
not affect the period
((T), as long as A ≠ 0.
U p
B o b
Bob
A 1
B o b
a 2
a 1
A 2
Bob
B o b
b c 1
c 2
A 1
T I M E
b b
O n e C y c l e
T
a 1
a 2
c 1
c 2
a 1
a 2A 2
A 1
A 2

5.  What is meant byWhat is meant by
Phase?
 The top graphThe top graph
represents two bobsrepresents two bobs
that are in-phase withthat are in-phase with
each other,each other, ∠∠ θ’s’s areare
equal as are theequal as are the
amplitudes (amplitudes (A) and) and
DOM of the bobs.of the bobs.
 In the bottom graph,In the bottom graph,
the two bobs havethe two bobs have
opposite phase. We. We
can also say the bobscan also say the bobs
areare completely out ofout of
phase or are out ofphase or are out of
phase byphase by π (why?).(why?).
U p
B o b
A
B o b
A
O n e C y c le
A
A
T IM E
B o b # 2
T
B o b # 1
U p
B o b
# 1
A
B o b
# 2
A

6.  The frequency of a pendulum has been has beenThe frequency of a pendulum has been has been
found to be:found to be: f = ((g/L)½
)/(2π). Here,Here, g == 9.81 m/s2
andand L is the length of the pendulum cord (to theis the length of the pendulum cord (to the
centre of the bob) measured in metres (m). Thecentre of the bob) measured in metres (m). The
value found from this equation is called thevalue found from this equation is called the
natural frequency which iswhich is independent of theindependent of the
massmass of the bob and there can only beof the bob and there can only be one value.value.
The frequency is alsoThe frequency is also independent of theindependent of the
amplitudeamplitude, but the, but the ∠∠ the cord makes with thethe cord makes with the
normal must be reasonably small.normal must be reasonably small.
 Recall thatRecall that f = 1/T, so the period can be easilyso the period can be easily
found from the natural frequency.found from the natural frequency.
 Motion of a pendulum bob and motion of a bobMotion of a pendulum bob and motion of a bob
attached to a spring, which can be either verticalattached to a spring, which can be either vertical
or horizontal (bob would have to be on aor horizontal (bob would have to be on a
frictionless surface) is calledfrictionless surface) is called periodic motion andand
often referred to asoften referred to as simple harmonic motion..

7.  Resonance, as defined by your text, occurs when energy isas defined by your text, occurs when energy is
added to a vibrating system at the same frequency as theadded to a vibrating system at the same frequency as the
natural frequency (of the system) and with the same phasenatural frequency (of the system) and with the same phase
(as the system). Energy of the system (the child)(as the system). Energy of the system (the child) may
continuously increase but this depends on energy losses. Incontinuously increase but this depends on energy losses. In
the graph below, the increase in energy is represented by thethe graph below, the increase in energy is represented by the
____________ in ________ .____________ in ________ .
 (How would the child have to be pushed?)
F
Amplitude R e s t P o s i t i o n
T I M E
T
T

8. Resonance Video, Demonstration
and Practice Questions
 The Tacoma Narrows bridge collapse in 1940 was
due to resonance created by wind.
 http://www.youtube.com/watch?v=j-zczJXSxnw
 Demonstration of “singing rods”.
Nelson Textbook:
Page 380 # 1, 4 Page 409 #24 – 27
Page 432 #1b,c & 3