PHYS 1001: Oscillations and Waves Stream 3&4: Dr Rongkun Zheng Dr Darren Hudson Streams 1&2: Dr Helen Johnston Rm 213. Ph:

My research: 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

What is an oscillation?

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 (ω) –Amplitude (A) What is an oscillation? §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? 1. position 1 2. position 2 3. position 3 4. position 4 5. position 5

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

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

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!) §14.2

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

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

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

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

Next lecture Applications of SHM Read §14.1–14.3