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# UPII-Wk4 - University Physics II Announcements Oscillations...

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April 16, 2008 University Physics II • Announcements • Oscillations Simple Harmonic Motion CLICKERS TO CHAN. 13

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April 16, 2008 Announcements Thanks for doing the Reading Quiz! PS3 due NOW (or to my box by the end of the day) Lab Report Due Friday by 5pm
April 16, 2008 Oscillations What do we mean by “oscillations”? Repeating motion Clock pendulum Marble in a bowl Loudspeaker diaphragm Guitar string Atoms in solids Air molecules Electrons in antennas • …

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April 16, 2008 Simple Harmonic Motion Common oscillation: – Mass attached to a spring – Trigonometric functions – Simple harmonic motion (SHM) Typically small deviations from the equilibrium position Mass on a spring – Pendulum Periodic motion
April 16, 2008 -1.5 -1 -0.5 0 0.5 1 1.5 0 2 4 6 8 10 12 Trigonometric Functions Trigonometric functions are periodic (sin and cos) Period is 2 π Functions are related by the phase angle -1.5 -1 -0.5 0 0.5 1 1.5 0 2 4 6 8 10 12 sin θ 2 π cos ( θ - π /2) ( 29 cos / 2 sin θ π θ - = -80 -60 -40 -20 0 20 40 60 80 0 0.2 0.4 0.6 0.8 1 1.2 cos

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April 16, 2008 Question #1 An object can oscillate around 1. Any equilibrium point 2. Any stable equilibrium point 3. Certain stable equilibrium points 4. Any point provided the forces exerted obey Hooke’s law 5. Any point
April 16, 2008 Simple Harmonic Motion SHM can be described by trigonometric functions General presentation A – amplitude (maximum displacement in either direction) φ phase angle (radians) T – period of motion ( 29 ( ) cos x t A t ϖ φ = + -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 -2 0 2 4 6 8 10 x t A φ T

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April 16, 2008 Simple Harmonic Motion/2 ω – angular frequency What is its meaning? Displacement is repeated after T : Trigonometric functions repeat after: Angular frequency Linear frequency is also used ( 29 ( ) ( ) cos cos x t x t T A t A t T ϖ ϖ = + = + ( 29 2 t T t ϖ ϖ π + = + 2 T ϖ π = 2 T π ϖ = [ ] 1 2 Hz f f T ϖ π = = =
April 16, 2008 Question #2 A mass attached to a spring oscillates back and forth as indicated in the position vs. time plot below. 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 (+ or -)

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UPII-Wk4 - University Physics II Announcements Oscillations...

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