Chapter 14 Oscillations

Introduction Oscillations of a Spring (Hands-on emphasis) Simple Harmonic Motion (Mathematical emphasis) Pendulums - Simple & beyond simple Damped Harmonic Motion (Modeling emphasis) Driven Damped Harmonic Motion & Resonance (the grand finale)

Oscillations of a Spring Characteristics –Amplitude –Period –Frequency –Phase Discovery Lab (Handout) Question

Simple Harmonic Motion Mathematical Representation –Equation of motion (Simple common phenomenon using Classical Mechanics) –Solution exerciseexercise –Role of initial conditions –Phase angle –Angular frequency and frequency –Natural frequency –QuestionQuestion

…SHM cont’d. Relation to Uniform Circular Motion –Physlet I16.1 Usefulness –good approximation –component of any oscillation Physlet I16.5

Energy and SHM Kinetic energy of object in SHM Spring potential energy Physlet I16.3 Potential energy graphical representation –Whiteboard exercise Jeopardy problems Question

Pendulums Simple pendulum –Equation of motion –Approximation sin(θ) ≈ θ Handout Physlet I16.2 –Solution –QuestionQuestion Physical Pendulum –QuestionQuestion Torsion Pendulum

Damped Harmonic Motion Equation of motion and solution –Damping –Over-damped, Under-damped, Critical damping Physlet E16.6 Mathematical modeling –Stella model (later)

Driven Damped Harmonic Motion & Resonance Driven (Forced) situations Equation of motion and solution Mathematical modeling continued Resonance –What? and When? –Examples (including “field trip”) –Q-value Physlet E16.7

the end

Is the function Asin(ωt + ø) a solution of the general simple harmonic motion equation? If so, what are the constraints on ω, A and ø? back

To what question is this the answer? (1/2)(1kg)v 2 = (1/2)(2N/m)(.2m) 2 next back

To what question is this the answer? (1/2)(1kg)v 2 + (1/2)(1N/m)(-.2m) 2 = (1/2)(1N/m)(.4m) 2 next back

To what question is this the answer? (1/2)(3N/m)x 2 = (1/2)(1kg)(1m/s) 2 next back

To what question is this the answer? (1/2)(2N/m)(.2m) 2 = (1/2)(1N/m)x 2 next back

To what question is this the answer? (1/2)(1kg)(2m/s) 2 = (1/2)k(2m) 2 back

At the point P, the mass has _______ and _______. 1)v>0, a>0 2) v=0, a>0 3) v 0 4) v>0, a=0 5) v=0, a=0 6) v<0, a=0 7) v>0, a<0 8) v=0, a<0 9) v<0, a<0 back

5N/m 1kg 0.4m stretch 1N/m 1kg 0.5m stretch 5N/m 2kg 0.2m stretch 4N/m 5kg 0.2m stretch 4N/m 4kg 0.5m stretch 1N/m 5kg 0.5m stretch Rank on the basis of time to complete one cycle. (Least to greatest) backback A B C D E F

A mass is hanging in equilibrium via a spring. When it is pulled down, what happens to the total potential energy (gravity + spring)? 1)It increases. 2)It stays the same. 3)It decreases. back

Physlet E16.5,6 resonance

Which falls faster? A: Meter stick B: Meter stick with heavy clamp 1)A 2)B 3)Same. 4)More info is needed. back

A pendulum is in an elevator that approaching the top floor of a building and is coming to a stop. What happens to the period of the pendulum? 1)It increases. 2)It stays the same. 3)It decreases. 4)More info is needed. back

angle in degrees angle in radians sine of angle tangent of angle cosine of angle Trigonometric Functions for Small Angles back back