PHYS1002 Fundamentals Module 3 OSCILLATIONS AND WAVES A/Prof Helen Johnston Room 213, A28 School of Physics h.johnston@sydney.edu.au The University of Sydney Page 1 My research: • black holes in binary star systems • supermassive black holes in the centres of galaxies The University of Sydney Page 2 Module content “College Physics” by Knight, Jones & Field: • • • • Chapter 14: Oscillations (Periodic motion) Chapter 15 : Travelling wave and sound Chapter 16 (parts): Superposition and standing waves Chapter 17 (parts): Wave optics Assignment 3: due Week 13 The University of Sydney Page 3 Course outline L1: Oscillations and Simple Harmonic Motion (SHM) L2: Properties of SHM; Simple Pendulum L3: Damped and Forced Oscillations; Resonance L4: Introduction to Waves L5: Descriptions of Waves L6: Superposition, interference and standing waves L7: Boundary conditions and normal modes L8: Sound as a wave L9: Perception of sound L10: Interference and beats L11: Light, refraction, diffraction and interference L12: Doppler effect, shock waves The University of Sydney Page 4 This lecture (L1) • Oscillations §14.1 473-474 • Linear restoring force (Hooke’s law) §8.3 266m-268t • Simple Harmonic Motion (SHM) §14.2,14.3 475-478 The University of Sydney Page 5 Maths reminder: Sines and cosines ๐ sin ๐ฅ = cos ๐ฅ ๐๐ฅ ๐ cos ๐ฅ = −sin ๐ฅ ๐๐ฅ The University of Sydney Page 6 What is an oscillation? The University of Sydney Page 7 What is an oscillation? Example: a marble rolling in a bowl A C B The University of Sydney Page 8 What is an oscillation? Example: a marble rolling in a bowl The University of Sydney Page 9 What is an oscillation? Any motion that repeats itself Described with reference to • an equilibrium position where the net force is zero • a restoring force which acts to return object to equilibrium The University of Sydney Page 10 Oscillatory motion Example: a marble rolling in a bowl – position vs. time The University of Sydney Page 11 Period, Frequency, and Amplitude • Period ๐ : time to complete one full cycle [s] • Frequency ๐ : number of cycles per second, ๐ = 1/๐ [Hz] • Angular frequency ๐ = 2๐๐ = 2๐/๐ [rad/s] The University of Sydney Page 12 The spring: Hooke’s law A spring which is stretched or compressed exerts a force. This force is proportional to the displacement of the end of the spring, and always points in the opposite direction. ๐น = −๐๐ฅ (Hooke’s law) ๐ is the spring constant: large for a stiff spring, small for a soft spring The University of Sydney Page 13 The University of Sydney Page 14 Motion of a mass on a spring What happens when we displace a mass on a spring from equilibrium and let go? We get an oscillation. The University of Sydney Page 15 The University of Sydney Page 16 Motion of a mass on a spring Oscillation about an equilibrium position with a linear restoring force is always sinusoidal. The University of Sydney Page 17 Simple harmonic motion Any system where the restoring force varies linearly with displacement from equilibrium ๐น(๐ก) = −๐๐ฅ(๐ก) results in an oscillation where the displacement, velocity and acceleration are all sinusoidal functions of time. Any such oscillation is called simple harmonic motion (SHM). The University of Sydney Page 18 Sinusoidal functions 2๐๐ก ๐ฅ ๐ก = ๐ด sin ๐ or 2๐๐ก ๐ฅ ๐ก = ๐ด cos ๐ The University of Sydney Page 19 Velocity and acceleration The position of the mass ๐ฅ is sinusoidal. What about ๐ฃ and ๐? Can you predict • where the velocity will be maximum? • where the velocity will be zero? • where the acceleration will be maximum? • where the acceleration will be zero? The University of Sydney Page 20 Velocity and acceleration The position of the mass ๐ฅ is sinusoidal. What about ๐ฃ and ๐? The University of Sydney Page 21 Describing SHM ๐ = 2๐๐ = 2๐ ๐ ๐ฆ ๐ก = ๐ด cos(๐๐ก) ๐ฆmax = ๐ด ๐ฃ ๐ก = −๐๐ด sin(๐๐ก) ๐ฃmax = ๐๐ด ๐ ๐ก = −๐! ๐ด cos ๐๐ก −๐of !Sydney ๐ฆ ๐ก The= University ๐max = ๐! ๐ด Page 22 Next lecture Next lecture: Properties of SHM, and the Simple Pendulum §Pre-reading: §14.2, 14.4, 14.5 The University of Sydney Page 23
