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Hookes Law

the amount of stretch or compression of an elastic material is directly proportional to the applied force

medium

A substance through which signals can travel (e.g. air for sound waves).

Mechanical wave

A wave that requires a medium through which to travel

Nodes

The points at which two waves cancel in a standing wave.

Antinodes

The positions on a standing wave where the largest amplitudes occur.

What is (mechanical) oscillation?

Oscillation is the repetitive variation, typically in time, of some measure about a central value (often a point of equilibrium) or between two or more different states. The term 'vibration' is precisely used to desc…

What is simple harmonic motion?

Oscillatory motion under a retarding force proportional to the amount of displacement from an equilibrium position. An object exhibits SHM only if the force F on it towards a point (the equilibrium position) is proporti…

What is a restoring force?

The restoring force is a function only of position of the mass or particle. It is always directed back toward the equilibrium position of the system. The restoring force is often referred to in si…

No, because the acceleration is not constant.

Do the usual equations of motion apply for SHM? Why?

What is the amplitude of an object in SHM?

The amplitude A is the maximum distance it reaches from the equilibrium position.

What is the period of an object in SHM?

The period T is the time for one oscillation (e.g. from y = A to y = -A and back to y = A).

What is the frequency of an object in SHM?

The frequency f of the motion is the number of oscillations in 1 s. (f = 1/T and T = 1/f)

What is the angular frequency of an object in SHM?

The angular frequency ω is given by ω = 2πf. This relates to the reference circle and circular motion.

maximum displacement

a

maximum velocity

vmax = Aω

maximum acceleration

amax = Aω²

(c) the maximum velocity of the falling tide

(a) The distance from one end of the motion to the other (3.6 m) is twice the amplitude. Therefore, A = 1.8 m.

<diagram>

Consider the point P as shown moving in a circle radius A about O with constant speed. Now consider the point Q as shown that moves up and down the vertical line between…

oscillation

any repeating motion

periodic motion

an oscillation that has the same time interval

pendulum

A device that swings back and forth due to the force of gravity

sec

units for T

they're inverses

how are frequency and period related to each other

240Hz

if f= 120Hz How many oscillations are there in 2sec

length and acceleration due to gravity

What does the period of a pendulum depend upon?

mass and spring constant

what does the period of an oscillating spring depend upon?

To increase the period...

you increase the length

natural frequency depends upon...

shape, size, and material

Resonance

a phenomenon that occurs when two objects naturally vibrate at the same frequency; the sound produced by one object causes the other object to vibrate

vibrations get larger and larger in Amplitude

what's the result of resonance, what do you achieve?

Transverse wave (ref notes)

The medium (middle) is vibrating perpendicular to the direction of the wave

longitudinal wave (ref notes)

the medium (middle) oscillates parallel to the direction of the wave

False

(T/F) Tycho Brahe was a Danish astronomer who confirmed Copernicus's theories by making many observations with his telescope.

True

Metallic bonds are formed with elements that have similar low electronegativities, true or false?

The quicker waves are produced the faster they travel.

False (if the medium is the same T is the same)

Isochronous

Having a frequency independent of amplitude.

restoring force

in a physics context, is a variable force that gives rise to an equilibrium in a physical system. If the system is perturbed away from the equilibrium, the restoring force will tend to bring…

Equilibrium Postition

The point at which there is no net force on the oscillator. For SHM this is the centre.

Elastic Strain Energy

The area under a Force vs Extension graph. SI unit: Joules

When the frequency doubles...

the maximum velocity doubles.

When the frequency halves...

the maximum acceleration quarters.

When the amplitude quadruples...

the maximum acceleration quadruples.

the time period doubles.

When the mass (on a spring) quadruples...

sound

_______ is a mechanical disturbance propagated through an elastic medium

inertia

_______ is the property of an object that leads it to resist any change in motion

elasticity

_______ is when an object returns to its initial/starting position after disturbance

vibrate

the combined properties of inertia & elasticity, causing an object to move back and forth from starting position and back again

sinusoid

_______ is the sound that results froma simple harmonic motion also known as pure tone

phase

_______ is the degree portion of a cycle at any given time

phase difference

_______ is the difference in phase angles at any given time

time

A measure of change between two events or moments.

sine wave

the waveform graph derived from simple harmonic motion is a _______

.001

1 millisecond= _______ second

pressure

_______ is the measure of force exerted on a unit area of surface

dyne

the unit of measure for pressure is the _______

watts

the unit of measure for power is _______

Power

(physics) the rate of doing work

wavelength frequency

_______ is inversely proportional to _______

.0002 2000

the dynamic range for pressure is _______ dyne/cm2 to _______ dyne/cm2

10-16 10-2

the dynamic range for power/intensity is _______ watt/cm2 to _______ watt/cm2

344

the constant for the wavelength formula is _______

amplitude time

the graph coordinates for waveform are _______ and _______

elasticity inertia

the properties of air that allow vibration are _______ and _______

brownian

Air consists of molecules in constant random motion, or _______ motion.

inertia elasticity

Air molecules have mass (_______) and spring (_______)

force/area

dyne/cm2=

energy/time/distance

watts/cm2=

reference

we use _______ because we want to compare to something that is the softest sound

0 140

the range of human hearing for dBIL is _______ to _______

loudness

amplitude is referring to the _______

pitch

frequency is referring to the _______

RMS

_______ amplitude refers to taking the square of all instantanous amplitudes, take the average of those squares, take the square root of the value of the most common measure of amplitude, particularly with the complex waveforms

344 frequency

wavelength= _______/_______

db

amplitude is measured in _______

HZ

frequency is measured in_______

degrees

Rotational Displacement can be measured in...

complex

we use RMS amplitude for _______ soun and is calculated because it is a more meaningful reference

rarefraction condensation

sound propagates through air through _______ and _______

wavlength

we can predict the frequency of sound from its distance traveled from the _______ formula

pressure intensity

the relationship between pressure and intensity is _______ squared = _______

20 to 20000HZ

the range for human hearing

Angular Velocity/Frequency

The rate of change of the angle

Time Period

The time required for one wave (T)

Angular acceleration

represented by a lower case alpha (α)

Displacement (in terms of Cosine/Sine)

x = Xcosωt (X = maximum particle displacement from mean position)

Velocity (in terms of Cosine/Sine)

v = ω(X^2 - x^2)^1/2

Examples of Oscillations

Mass on a spring (bungee jumping);

equilibrium

1)starting point of SHM, object is in _______, fnet equals zero

Displacement (for waves) (x)

The distance a particle moves in a particular direction from its mean (equilibrium) position.

Amplitude (for waves) (x₀)

Maximum displacement from the mean position

Frequency (F)

If you are given revolution per second or minute

Period (T)

the time for an object to complete one revolution

Simple Harmonic Motion (SHM)

Motion that takes place;

In phase

360 degrees or 2π off → When they overlap

Antiphase

180 degrees or π off → Frequencies cancel

out of phase

the crests of one wave overlap the troughs of another to produce regions of zero amplitude

Angular Frequency

Product of 2π and frequency;

What is harmonic motion?

When an object repeats its path at regular time intervals.

What is simple harmonic motion?

Harmonic motion that has a sinusoidal shape (sine or cosine) when the object's displacement is graphed as a function of time.

Where the object has zero net force acting on it.

What is the *equilibrium position* of an object in simple harmonic motion?

Where is the equilibrium position for a mass on a vertical spring?

Where the object would "naturally" hang because that's where the spring force and the gravitational force (weight) balance out to zero.

Where is the equilibrium position for a pendulum?

The lowest point of the swing (where the pendulum would "naturally" hang).

What is amplitude (A)?

An object's maximum displacement away from its equilibrium position.

What is the *amplitude* (A) on a graph of simple harmonic motion?

The vertical distance from the middle to the highest (peak) or the lowest (valley) point.

What is the *amplitude* for a spring?

The maximum distance the spring is stretched or compressed from its equilibrium position.

What is the *amplitude* for a pendulum?

The maximum angle the pendulum moves from its equilibrium position (the vertical).

What is period (T)?

The time it takes to complete one cycle of something (like a repeated path). In other words, the time it takes to return to the same position.

What is the *period* (T) on a graph of simple harmonic motion?

The interval between 2 similar points on the graph (for example, between 2 peaks or 2 valleys).

What is frequency (f)?

The number of cycles that occur in one second.

Hertz (Hz).

What is the unit for *frequency* (f)?

They're reciprocals.

How are *period* and *frequency* related to each other?

One back and forth oscillation.

For a spring or a pendulum, what is typically considered to be one cycle of motion?

What is the *restoring force*?

The force that acts to "restore" or return an object to its equilibrium position.

(aka, Hooke's Law)

F = restoring force

0

0

What does the negative sign in Hooke's Law (F = -kx) mean?

The negative sign reminds you that the force acts to reverse or negate the displacement.

The stiffness (of the spring).

What is the spring constant (k) sometimes called?

U = elastic potential energy

(aka, work required to stretch or compress a spring)

Is acceleration constant during simple harmonic motion?

No. The acceleration changes from a maximum at the amplitude (maximum displacement) to zero at the equilibrium position.

At maximum displacement from the equilibrium position (the amplitude).

When does a spring or a pendulum experience a maximum net force?

At the equilibrium position.

When does a spring or a pendulum experience maximum velocity?

At the amplitude (maximum displacement from the equilibrium position).

When does a spring or a pendulum have maximum potential energy?

The spring constant.

On a graph of a spring's restoring force versus its displacement, what does the *slope* of the graph represent?

The elastic potential energy. Or the work required to stretch or compress the spring.

On a graph of a spring's restoring force versus its displacement, what does the *area* under the curve represent?

T = period

period of a spring

Increase.

How will a heavier mass affect the period of a spring?

How will a heavier mass affect the period of a pendulum?

No effect. The period of a pendulum doesn't depend on mass.

Decrease.

How will a lighter mass affect the period of a spring?

How will less gravity affect the period of a spring?

No effect. The period of a spring doesn't depend on gravity.

What is damped harmonic motion?

When the amplitude decreases over time.

Displacement, x

The change of position with direction (either positive or negative) from the equilibrium

Amplitude, A

Maximum displacement

Time Period, T

The time taken for one complete cycle of an oscillation and is equal to the reciprocal of frequency (1/f). The unit is the second (s)

Frequency, f

The number of complete cycles in one second and is equal to the reciprocal of time period (1/T). The unit is the Hertz (Hz).

Angular Frequency, ω

The size of the angle turned through in one second (2π/T).

Phase Difference Equation

2 π t / T, where t is time elapsed (delta t) and T is time period

Free Oscillations

The amplitude is constant and no frictional forces are present.

Displacement-Time graph

Sinusoidal shape that cuts through the x-axis as the object pass equilibrium. The gradient indicates the velocity at that point in time.

Velocity-Time graph

Sinusoidal shape that cuts through the x-axis when the object is at maximum displacement. The gradient indicates the acceleration at that point in time.

Acceleration-Time Graph

Sinusoidal shape that cuts through the x-axis as the object pass equilibrium. Out of phase by π compare with displacement-time graph.

SHM Acceleration Equation

a = -(2 π f)² x

SHM Velocity Equation

v = ±2 π f √(A² - x²)

SHM Displacement Equation

x = A cos(2 π f t)

Spring Time Period

T = 2 π√(m/k), where m is object mass and k is spring constant

Pendulum Time Period

T = 2 π√(L/g), where L is the length of the pendulum and g is gravitational field strength

Light Damping

The time period remains constant and the amplitude gradually decreases.

Critical Damping

damping which stops the motion of an oscillating particle in minimum time.

Heavy Damping

No oscillation occurs, returns to equilibrium slowly.

Forced Oscillations

Occurs when a periodic force is applied

Periodic Force

A force that is applied at regular intervals