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PHYS 1001: Oscillations and Waves

PHYS 1001: Oscillations and Waves. Stream 3&4: Dr Rongkun Zheng Dr Darren Hudson rongkun.zheng@sydney.edu.au d.hudson@sydney.edu.au. Streams 1&2: Dr Helen Johnston Rm 213. Ph : 9036-9259 h.johnston@physics.usyd.edu.au. My research: black holes in binary star systems

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PHYS 1001: Oscillations and Waves

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  1. PHYS 1001:Oscillations and Waves Stream 3&4: DrRongkunZheng Dr Darren Hudson rongkun.zheng@sydney.edu.au d.hudson@sydney.edu.au Streams 1&2: DrHelen Johnston Rm 213. Ph: 9036-9259 h.johnston@physics.usyd.edu.au

  2. My research: • black holes in binary star systems • supermassive black holes in the centres of galaxies

  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

  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

  5. What is an oscillation?

  6. What is an oscillation? • 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

  7. Test your understanding • Consider five positions of the mass as it oscillates: 1, 2, 3, 4, 5 (1) (2) (3) (4) (5)

  8. Where is the acceleration of the block greatest? • position 1 • position 2 • position 3 • position 4 • position 5

  9. Test your understanding • A mass attached to a spring oscillates back and forth as indicated in the position vs. time plot below.

  10. 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

  11. Simple Harmonic Motion • 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

  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. §14.2 12

  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. 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?

  14. Period and Amplitude Identical Periods Different Amplitudes Identical Amplitudes Different Periods §14.1

  15. Next lecture • Applications of SHM • Read §14.1–14.3

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