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PHYS 1001:Oscillations and Waves

Stream 3&4:

DrRongkunZheng

Dr Darren Hudson

Streams 1&2:

DrHelen Johnston

Rm 213. Ph: 9036-9259

- black holes in binary star systems
- supermassive black holes in the centres of galaxies

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

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

- Any motion that repeats itself
- Described with reference to anequilibrium positionwhere the net force is zero, and arestoring forcewhich acts to return object to equilibrium
- Characterised by:
- Period (T) or frequency (f) or angular freq (ω)
- Amplitude (A)

§14.1

Test your understanding

- Consider five positions of the mass as it oscillates: 1, 2, 3, 4, 5

(1) (2) (3) (4) (5)

Where is the acceleration of the block greatest?

- position 1
- position 2
- position 3
- position 4
- position 5

Test your understanding

- A mass attached to a spring oscillates back and forth as indicated in the position vs. time plot below.

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 acceleration

- Suppose the restoring force varies linearly with displacement from equilibriumF(t) = –kx(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!)

§14.2

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.

§14.2

12

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.

d

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?

Next lecture

- Applications of SHM
- Read §14.1–14.3

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