View
18
Download
0
Category
Tags:
Preview:
DESCRIPTION
PHYS16 – Lecture 32. Ch. 15 Oscillations . Oscillations pre-question. Is a bouncing ball an example of simple harmonic motion? Yes No. Oscillations pre-question. - PowerPoint PPT Presentation
Citation preview
PHYS16 – Lecture 32
Ch. 15 Oscillations
Oscillations pre-question
• Is a bouncing ball an example of simple harmonic motion?
A) YesB) 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 kidB) The skinny kidC) The kid who pushes off the ground the bestD) Both complete in the same time
Outline for Oscillations
• Simple Harmonic Motion– Position, Velocity, Acceleration– Force– Energy
• Resonance and Damping
Oscillations and Periodic Motion
http://img.tfd.com/ggse/c9/gsed_0001_0012_0_img2993.png
Simple Harmonic Motion
1) About Equil.2) Periodic3) Sinusoidal
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
T
tAx
2
)sin(
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?
)cos()90sin()sin(
tAtAxtAx
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 cosinewith a φ=0 degrees.
SHM Position, Velocity, Acceleration
http://www.tutornext.com/system/files/u89/Chapter%2011-3.gif
)sin(
)cos(
)sin(
2 tAa
tAv
tAx
Discussion
• What is the max speed and when does it occur?
Equilibrium Point
/2at t 0 0at t max
v
Av
Example Question
• An object undergoes simple harmonic motion. If the amplitude and period are doubled, the object’s max speed is:
A) QuadrupledB) DoubledC) UnchangedD) HalvedE) 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
xkxF ˆ
http://www.cs.wright.edu/~jslater/SDTCOutreachWebsite/images/gif/spring_mass_dia.gif
Restoring Force – Spring
mkf
mk
xmkx
tAmtAk
xkxF
21 ,
)sin()sin(dtdmma
2
2
2
2
Discussion: Period
• A block on a spring has a period of T. What is the period if:
A) the mass is doubled?
B) k is quadrupled?
C) A is doubled?
T2
T21
T
Restoring Force - Pendulum• What is the period of a pendulum?
http://upload.wikimedia.org/wikipedia/en/thumb/a/a8/Pendulum.png/300px-Pendulum.png
Lg
smallfor ,
)sin(
Lsmgks
mgksF
Simple Harmonic Motion:Energy
Energy in SHM
2
22222
22
21
)(cos21)(sin
21
21
21
kAE
tAktAmE
kxmvE
http://www.farraguttn.com/science/milligan/APPhys/SHMOver_files/image022.jpg
Main Points - SHM
• Movement
• Restoring Force creates oscillation
• Energy is dependent on amplitude
)sin( tAx
2
2
dtxdmkxF
2
21 kAE
Recommended