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

add not destroy

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

Add them together

**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

that describe these standing waves

Harmonics

and overtones

**n Harmonics overtones**

1 1 fundamental

2 2 1

3 3 2

4 4 3

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

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

D. Quadruples

E. Quarters

"I saw in the reading that we will be doing more problems with springs, can we go over those again?"

" Why is amplitude not related to those other terms on the prequiz? Question 4. "

"Which of these is not related to the others

Frequency Amplitude Period Wavelength Velocity"

"How are we able to tell the velocity of waves?"

"I still don't understand what harmonic motion is. Could we go over this in class?"