PHYS16 – Lecture 32 Ch. 15 Oscillations

Oscillations pre-question Is a bouncing ball an example of simple harmonic motion? Yes No

Oscillations pre-question Two kids are swinging on two swings of the same height – one kid is a little chubbier than the other. Neglecting frictional forces, which kid completes a back and forth swing in the fastest time? A) The chubby kid B) The skinny kid C) The kid who pushes off the ground the best D) Both complete in the same time

Outline for Oscillations Simple Harmonic Motion Position, Velocity, Acceleration Force Energy Resonance and Damping

Oscillations and Periodic Motion Simple Harmonic Motion 1) About Equil. 2) Periodic 3) Sinusoidal http://img.tfd.com/ggse/c9/gsed_0001_0012_0_img2993.png

Discussion: Examples of SHM? Mass on a Spring Pendulum Snowboarder in halfpipe Bungee jumper Child on swing Bobble head doll?

Simple Harmonic Motion: Position, Velocity, Acceleration

Simple Harmonic Motion Equilibrium Point http://www.gailruby.com/Picture4.png

Discussion: Phase Your book says that displacement is in terms of cosine and I just said that it is in terms of sine? Who is right? There is also a phase term (φ) that let’s you set the initial condition. If the oscillation starts at A it is a sine with a φ=90 degrees or a cosine with a φ=0 degrees.

SHM Position, Velocity, Acceleration http://www.tutornext.com/system/files/u89/Chapter%2011-3.gif

Discussion What is the max speed and when does it occur? Equilibrium Point

Example Question An object undergoes simple harmonic motion. If the amplitude and period are doubled, the object’s max speed is: Quadrupled Doubled Unchanged Halved Quartered

Simple Harmonic Motion: Restoring Force

Restoring Force Force that always points back to the equilibrium position – Example = spring k is just a constant – for a spring it is the spring constant http://www.cs.wright.edu/~jslater/SDTCOutreachWebsite/images/gif/spring_mass_dia.gif

Restoring Force – Spring

Discussion: Period A block on a spring has a period of T. What is the period if: the mass is doubled? k is quadrupled? A is doubled?

Restoring Force - Pendulum What is the period of a pendulum? http://upload.wikimedia.org/wikipedia/en/thumb/a/a8/Pendulum.png/300px-Pendulum.png

Simple Harmonic Motion: Energy

Energy in SHM http://www.farraguttn.com/science/milligan/APPhys/SHMOver_files/image022.jpg

Main Points - SHM Movement Restoring Force creates oscillation Energy is dependent on amplitude