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# LPH 105 W15 11:intro

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## Richard Datwyler

on 21 June 2016

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#### Transcript of LPH 105 W15 11:intro

SHM
Energy in SHM
Oscillation
Pendulum
amplitude, frequency, period
Kinetic and potential
Equations of motion
dampened and resonance
Wave motion
Intensity and power
Superposition, interference, and standing waves
types of waves
Energy, relationships
Simple Harmonic Oscillator
Describe its motion
A spring is an easy example (DEMO)

Repeats, constant in time, distance it travels, speed maximizes
Frequency, period, amplitude, velocity
SHO
Frequency = repetitions per second
units = Hertz = 1/s
period = how long it takes to repeat a cycle
units = second
amplitude = distance traveled from equilibrium
simple = frequency is constant
harmonic = motion is sinusoidal (like a sine wave)
oscillation = move back and forth over same path
SHO
Energy
Note it is faster at places, and it has great displacement at other.
Thus it has KE and PE. And they also cycle back and forth, and between each other.
at some location it has only KE.
at other locations only PE.
But the total energy is constant throughout.
Energy
If you are in between the max, you will have both KE and PE
Thus you will have a velocity, at a location away from the equilibrium, and they are related.
With the max velocity and the max position listed as.
x = A
max
One more analysis
Because we can equate the max KE and PE, we can solve for a relationship of period and frequency
Wave equation
Because the motion is harmonic (like a sine wave) we can describe its position as:
And describe its velocity as:
And acceleration as... ( won't do this one)
Pendulum
Without the fan fare a pendulum is an oscillator and it moves similar to a spring.
Its energies are the same, but period and frequency are as follows.
Notice the mass of the pendulum is irrelevant.
Pendulum
over damp
under damp
critically damped
driven
resonance
Waves
Amplitude
Wavelength
Frequency
Period
Velocity
special case of wave on a string
Types of waves
Longitudinal
Transverse
oscillation in direction of wave motion
oscillation 90 degrees to wave motion
Mechanical
Electromagnetic (light)
Intensity
DEMO
Candle or sound
decreases with distance
Solve for constants, and relate.
Traveling waves
Boundary conditions
Superposition
fixed and free
Standing wave
Made from two waves, one going to right, other left
'standing' means long lived, or constant shape
Node = no motion
anti node = most motion
DEMO
different standing waves can be made, depending on frequency and wavelength.
For some unknown reason to me, we have two terms
that describe these standing waves
Harmonics
and overtones

n Harmonics overtones
1 1 fundamental
2 2 1
3 3 2
4 4 3

If my fundamental
Frequency is 100 Hz
and I produces another
standing wave that is 400 Hz
which Harmonic is it?
A. 1
B. 2
C. 3
D. 4
E. 5

Which of these is not a SHO
A. Mass on spring
B. Pendulum
C. Wheel
D. Car on circular race track
E. Clock
Which of these would increase the time it takes for a mass to return to where it started?
A. Give it a larger initial displacement
B. Increase the spring constant
C. Increase the mass
D. Decrease the mass
E. Increase the frequency
Where is the potential energy of a pendulum the greatest?
A. Where the kinetic energy is negative
B. Where the kinetic energy is positive
C. Where the kinetic energy is zero
D. At the bottom of its swing
E. Depends on where you call y = zero
If I cut the distance I am away from a source in half what happens to the intensity?
A. Doubles
B. Stays same
C. Halves