Oscillations and Waves Stream 3amp4 Dr Rongkun Zheng Dr Darren Hudson rongkunzhengsydneyeduau dhudsonsydneyeduau Streams 1amp2 Dr Helen Johnston Rm 213 Ph ID: 356004
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Slide1
PHYS 1001:Oscillations and Waves
Stream
3&4: Dr Rongkun ZhengDr Darren Hudsonrongkun.zheng@sydney.edu.aud.hudson@sydney.edu.au
Streams 1&2:
Dr
Helen Johnston
Rm
213.
Ph
: 9036-9259
h.johnston@physics.usyd.edu.auSlide2
My research:
black holes in binary star systems
supermassive black holes in the centres of galaxiesSlide3
Module Outline
10 LecturesLab + tutorials + assignments Assignment #6 due 7 June
“University Physics”, Young & FreedmanCh. 14: Periodic MotionCh. 15: Mechanical WavesCh. 16: Sound and HearingSlide4
OverviewL1: Intro to Simple Harmonic Motion (SHM)
L2: Applications of SHM; Energy of OscillationsL3: Simple and Physical Pendulums; ResonanceL4: Intro to Mechanical Waves
L5: Wave Equation and Wave SpeedL6: Interference and SuperpositionL7: Standing Waves; Normal ModesL8: Sound Waves; Perception of SoundL9: Interference; BeatsL10: Doppler Effect; Shock WavesSlide5
What is an oscillation?Slide6
Any motion that repeats itselfDescribed with reference to an
equilibrium position
where the net force is zero, and a restoring force which acts to return object to equilibriumCharacterised by:Period (T) or frequency (f) or angular freq (ω)Amplitude (A)What is an oscillation?
§14.1Slide7
Test your understanding
Consider five positions of the mass as it oscillates: 1, 2, 3, 4, 5
(1) (2) (3) (4) (5)Slide8
Where is the acceleration of the block greatest?
position 1position 2
position 3position 4position 5Slide9
A mass attached to a spring oscillates back and forth as indicated in the position vs. time plot below.
Test your understandingSlide10
A mass attached to a spring oscillates back and forth. At point P, the mass has
positive velocity and positive acceleration.positive velocity and negative acceleration.
positive velocity and zero acceleration.negative velocity and positive acceleration.negative velocity and negative acceleration.negative velocity and zero acceleration.zero velocity but is accelerating (positively or negatively).zero velocity and zero accelerationSlide11
Simple Harmonic Motion
Suppose the
restoring force varies linearly with displacement from equilibrium F(t) = –k x(t)Then the displacement, velocity, and acceleration are all sinusoidal
functions of time
This defines Simple Harmonic Motion
(SHM)
Period/frequency depend
only
on
k
and
m
with
ω = √(
k
/
m
)
(does not depend on amplitude!)
§14.2Slide12
12
SHM & circular motion
An object moves with uniform angular velocity ω in a circle.The projection of the motion onto the
x
-axis is
x
(
t
) =
A
cos(
ωt
+
φ
)
The projected velocity & acceleration also agree with SHM.
Every kind of SHM can be related to a motion around an equivalent reference circle.
§14.2Slide13
A block on a frictionless table is attached to a wall with a spring. The block is pulled a distance
d to the right of its equilibrium position and released from rest. It takes a time t to get back to the equilibrium point.
If instead the mass is pulled a distance 2d to the right and then released from rest, how long will it take to get back to the equilibrium point?dSlide14
If instead the mass is pulled a distance 2d
to the right and then released from rest, how long will it take to get back to the equilibrium point?twice as long
the square root of two times longerthe samethe square root of two times shortertwice as shortSlide15
Identical Periods
Different Amplitudes
Identical AmplitudesDifferent PeriodsPeriod and Amplitude§14.1Slide16
Next lectureApplications of SHM
Read §14.1–14.3