Post on 22-Dec-2015
transcript
Extreme ExampleExtreme Example
Tacoma Narrows BridgeTacoma Narrows Bridge It stood for only 3 months before….It stood for only 3 months before….
http://www.youtube.com/watch?v=P0Fi1VcbpAI
Vibrations and wavesVibrations and waves
SHM SHM OscillationOscillation
PeriodicPeriodic
f= -KXf= -KXF= Restoring forceF= Restoring force
K= spring constantK= spring constant
X= displacementX= displacement
F= Restoring forceF= Restoring force
K= spring constantK= spring constant
X= displacementX= displacement
Equilibrium PositionEquilibrium Position DisplacementDisplacement
AmplitudeAmplitude Period-T, time needed for 1 full Period-T, time needed for 1 full
cycle (sec)cycle (sec) Frequency- f, # of cycles per Frequency- f, # of cycles per
second (Hz)second (Hz)
f= 1/T T= f= 1/T T= 1/f1/f
*Car Spring Example, pg. 311*Car Spring Example, pg. 311Section 11-2
Section 11-2 draws draws heavily from
heavily from chpt. 6chpt. 6
Read on your
Read on your
own pg. 312-own pg. 312-
314314
Section 11-3, read the deriving Section 11-3, read the deriving of formula…of formula…
TTss = 2 = 2 m/k m/k Formula for Formula for Period of Period of
SpringSpringm= massm= mass
k= spring k= spring constantconstant
Not direct relationship!Not direct relationship!
T m/kT m/k Mass must QUADRUPLE to double Mass must QUADRUPLE to double
periodperiod We can Substitute…We can Substitute…
f = 1/T = f = 1/2f = 1/T = f = 1/2 k/m k/m
What are What are T & fT & f of the car of the car example on pg.311 after example on pg.311 after hitting a bump? Assume shock hitting a bump? Assume shock absorbers are poor so car absorbers are poor so car really oscillates a lot. really oscillates a lot.
T = 2T = 2 √m/k√m/k = 6.28 = 6.28 √√1400kg/ 1400kg/ 6500N/m6500N/m
=.92sec =.92sec
F = 1/.92F = 1/.92 = 1.09Hz= 1.09Hz
A small insect (.3g) is A small insect (.3g) is caught in a spider web caught in a spider web (mass-less). The web (mass-less). The web vibrates at 15Hzvibrates at 15Hz
a.a. estimate the value of K estimate the value of K for the webfor the web
b.b. find f for an insect of find f for an insect of mass .1g.mass .1g.
f = 1/2f = 1/2 √K/m√K/m
K = (2K = (2f)f)22mm= (6.26 x 15)= (6.26 x 15)22 (3 x 10 (3 x 10-4-4kg)kg)
2.7 N/m2.7 N/m
Sub in for MSub in for M
1 x 101 x 10--
44kgkgf = 26Hzf = 26Hz
Simple PendulumSimple Pendulum
What determines T for a What determines T for a Pendulum?Pendulum?
Mass of bobMass of bobAmplitude of swingAmplitude of swing
Length of stringLength of stringGravity of locationGravity of location
××××
FormulaFormula
TTpp = 2 = 2 √√LL//gg
F = F = 11//TT = ½ = ½ √√gg//LL
For pendulums to be said to be in SHM the For pendulums to be said to be in SHM the displacement angle has to be small- less than displacement angle has to be small- less than
1515°°
For pendulums to be said to be in SHM the For pendulums to be said to be in SHM the displacement angle has to be small- less than displacement angle has to be small- less than
1515°°
Damped Harmonic Damped Harmonic MotionMotion
Amplitude of a swinging spring Amplitude of a swinging spring on a pendulum slowly on a pendulum slowly
decreases in time until the decreases in time until the oscillations stop all together. oscillations stop all together.
XXTimeTime
Damping is caused by air Damping is caused by air friction and internal friction and internal
friction within the systemfriction within the system Common dampening Common dampening
systems are shock systems are shock absorbers and door absorbers and door
closing mechanisms.closing mechanisms.
A = over damped (too slow)A = over damped (too slow)
B= Critically dampedB= Critically damped
C=under damped (still C=under damped (still oscillating)oscillating)
CC
BB
AAx
time
Resonance… Forced Resonance… Forced Vibrations Vibrations
Objects have Objects have natural natural resonant frequenciesresonant frequencies. .
When vibrations are put When vibrations are put on an object that are at on an object that are at
the the natural resonant natural resonant frequencyfrequency, an , an increaseincrease in in amplitudeamplitude is observed. is observed.
If pushing is random- swing If pushing is random- swing just bounces aroundjust bounces around
But if you push with frequency But if you push with frequency equal to Natural Resonant equal to Natural Resonant Frequency(NRF) you can get a Frequency(NRF) you can get a big amplitudebig amplitude
SwingSwing
Wave MotionWave Motion mechanical waves for now…mechanical waves for now… -OVER HEAD- -OVER HEAD-
Is the velocity of a wave moving Is the velocity of a wave moving along a cord the same as the along a cord the same as the velocity of a particle of the cord?velocity of a particle of the cord?
NO – velocities are different so are directions…
Types of wavesTypes of waves
Wave Wave MotionMotion
Wave Wave MotionMotion
Transverse Transverse
CompressionCompression
Rare Rare factionsfactions
Longitudinal Longitudinal
S- wavesS- waves Earth quake Earth quake waveswaves
P- waves; only P P- waves; only P travels through travels through
liquidliquid
Wave InterferenceWave Interference
•Principle of superposition
•Destructive interference
•Constructive Interference
•In phase or Out of phase
Standing Waves: Standing Waves: ResonanceResonance
•Standing Waves
•Nodes
•Antinodes
•Natural frequencies
•Fundamental frequencies
•Overtones
http://www.youtube.com/watch?feature=player_embedded&v=Oz53w_k_j_A#!