My research: black holes in binary star systems supermassive
black holes in the centres of galaxies
Slide 3
Module Outline 10 Lectures Lab + tutorials + assignments
Assignment #6 due 7 June University Physics, Young & Freedman
Ch. 14: Periodic Motion Ch. 15: Mechanical Waves Ch. 16: Sound and
Hearing
Slide 4
Overview L1: Intro to Simple Harmonic Motion (SHM) L2:
Applications of SHM; Energy of Oscillations L3: Simple and Physical
Pendulums; Resonance L4: Intro to Mechanical Waves L5: Wave
Equation and Wave Speed L6: Interference and Superposition L7:
Standing Waves; Normal Modes L8: Sound Waves; Perception of Sound
L9: Interference; Beats L10: Doppler Effect; Shock Waves
Slide 5
What is an oscillation?
Slide 6
Any motion that repeats itself Described with reference to an
equilibrium position where the net force is zero, and a restoring
force which acts to return object to equilibrium Characterised by:
Period (T) or frequency (f) or angular freq () Amplitude (A) What
is an oscillation? 14.1
Slide 7
Test your understanding Consider five positions of the mass as
it oscillates: 1, 2, 3, 4, 5 (1) (2) (3) (4) (5)
Slide 8
Where is the acceleration of the block greatest? 1. position 1
2. position 2 3. position 3 4. position 4 5. position 5
Slide 9
A mass attached to a spring oscillates back and forth as
indicated in the position vs. time plot below. Test your
understanding
Slide 10
A mass attached to a spring oscillates back and forth. At point
P, the mass has 1. positive velocity and positive acceleration. 2.
positive velocity and negative acceleration. 3. positive velocity
and zero acceleration. 4. negative velocity and positive
acceleration. 5. negative velocity and negative acceleration. 6.
negative velocity and zero acceleration. 7. zero velocity but is
accelerating (positively or negatively). 8. zero velocity and zero
acceleration
Slide 11
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 = ( k / m )
(does not depend on amplitude!) 14.2
Slide 12
12 SHM & circular motion An object moves with uniform
angular velocity in a circle. The projection of the motion onto the
x-axis is x(t) = A cos(t + ) The projected velocity &
acceleration also agree with SHM. Every kind of SHM can be related
to a motion around an equivalent reference circle. 14.2
Slide 13
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? d
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1. twice as long 2. the square root of two times longer 3. the
same 4. the square root of two times shorter 5. twice as short
Slide 15
Identical Periods Different Amplitudes Identical Amplitudes
Different Periods Period and Amplitude 14.1