phys16 – lecture 32 ch. 15 oscillations. oscillations pre-question is a bouncing ball an example...
TRANSCRIPT
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?
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(
tAtAx
tAx
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
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
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
T2
1
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
L
g
smallfor ,
)sin(
L
smgks
mgksF
Energy in SHM
2
22222
22
2
1
)(cos2
1)(sin
2
12
1
2
1
kAE
tAktAmE
kxmvE
http://www.farraguttn.com/science/milligan/APPhys/SHMOver_files/image022.jpg