Sections
An oscillation (see image) is some kind of periodic motion.
Vibration is practically a synomyn for oscillation
Periodic means in the motion repeats in a fixed period of time.
If there are N cycles in time Delta t = N periods, then
N cycles 1
f = ------------ = ---------
N periods period
The unit of frequency is inverse seconds or 1/second.
This has a unit of frequency has a special name the
hertz.
The hertz is familiar
from
radio frequencies
(see image).
Our physical laws tells us that certain motions should repeat in equal periods of the parameter time of those laws.
We define time to be measured by those periods.
This, of course, was done even before modern physical laws which can be said to have begun with Newton's laws (see image).
People used obvious repeating motions to measure time: originally astronomical cycles: e.g.,
Mechanical clocks (see image) (which depend on oscillators) synchronize with astronomical clocks.
Thus, when modern physical laws came along there was no ``Shock of the New'' in defining time.
Those motions which repeat mostly exactly according to our physical laws give us our best clocks: these are atomic clocks (see 2 images).
They are simply more exactly periodic according to physical laws than other oscillating systems.
Typically, in an oscillator there is some restoring force and a possible state of stable equilibrium.
In equilibrium, the forces are balanced and there is no accelerations and, in the rest frame of the system, no velocity.
The restoring force is what makes the stable equilibrium stable.
If a one adds perturbing kinetic energy, the system moves off the stable equilibrium and acquires some potential energy above the minimum (which is at the stable equilibrium point.
The restoring force tries to pull the system back to equilibrium---and succeeds unless the system breaks down somehow.
An oscillation is set up if the the restoring force overshoots the the stable equilibrium point.
The oscillation continues perpetually if there is no way to rid the system of the mechanical energy: i.e., the sum of kinetic energy and potential energy. With friction and other motion-resistive forces, however, the oscillation will damp out.
To keep oscillating, oscillators usually need a driver of some kind---and we'll see some examples.
Examples of oscillators:
A homely example of pendulum is a child (or even you or me) on swing (see images).
Let's consider a mass on a spring.
Answer 4 is right.
Amplitude is the maximum size of the distance from stable equilibrium in the oscillation.
For the a spring, the ``natural frequency'' is given by
f = [1/(2*pi)]*sqrt(k/m) ,
where k is the spring constant (a property of the individual spring),
and
m is the mass of the bob.
We are actually assuming an ideal spring which is itself massless.
The real name for ``natural frequency'' is
resonant frequency.
If you just strike a system and give a jolt of energy, it will tend to oscillate at its resonant frequency or one of its resonant frequencies.
Usually, if you drive a oscillator off resonant frequency the oscillations will tend to be small.
The system will somehow resist being driven.
If you try to drive a system at its resonant frequency, the oscillations will tend to get bigger and bigger.
Eventually, the oscillations can cause cause the system to break down.
A famous example of destruction of system by oscillations is the collapse of the original Tacoma Narrows Bridge (see images) across Tacoma narrows of Puget sound in Washington state where wind excited the oscillations.
It was a much more complex case of oscillation (see Wikipedia: Tacoma Narrows Bridge: Cause of Collapse).
In the case of a pendulum (see images), gravity acts as the restoring force.
Answer 3 is right.
f = [1/(2*pi)]*sqrt(g/L) ,
where g = approx 9.8 m/s**2 is the acceleration due to gravity
and
L is the length of the arm.
The
resonant frequency
is independent of
the amplitude
as it should be for
simple harmonic motion.
The independence of amplitude allowed pendulum clocks (see images) to be made very accurate clocks.
Pendulum clocks tended to maintain their frequency even if the DRIVER of the pendulum was not very accurate in timing and caused small variations in amplitude.
From their invention in 1656 until the 1930s, pendulum clocks were about the world's most accurate clocks.
Of course, nothing is simple.
A whole complex technology went into making pendulum clocks more and more accurate.
The driver of pendulum clock is an escapement (see image).
There is a whole complex technology into making better escapements.
The main idea is that the pendulum itself through locking of a gear (which is the driver) of some kind largely controls the driver and forces it to drive at the resonant frequency or nearly.
Another driven pendulum is our homely example of pendulum is a child (or even you or me) on swing (see images).
Answer 3 is right.
I'm not entirely sure how the swinger drives a swing, although it's a pretty common effect.
I rather think, the swinger can get the swing structure vibrating and that then feeds back to the swing.
Well 1 is certain, but 2 may have a role.
And after all my years of swinging, I don't know.
A tuning fork (see images) is in some respects a simple example of musical instrument.
Striking it starts the oscillation and internal resistive forces damp it out.
By repeated striking you can drive it---play it---but people don't usually do that.
A tuning fork has a resonant frequency of course.
Usually a strike will excite the resonant frequency primarily.
All the others damp out quickly.
This is, of course, the same thing that happens musical instruments are ``struck'' in whatever way.
Somehow the design of a tuning fork with the forked prongs leads to an especially strong pure frequency resonance
The solid body oscillation of a tuning fork makes (or excites) vibrations in the air that radiate outward from the tuning fork.
Answer 1.
Actually seismic waves are a very energetic kind of sound in a sense.
A string instrument is a set of vibrating strings.
The strings have their own resonant frequencies (multiple ones for each string actually) and when struck they oscillate in standing waves (see images) at those resonant frequencies.
The resonant frequencies are often called normal modes in this context.
When struck all kinds of waves can be generated in the string.
But only those that ``fit'' don't cancel out much and instead reinforce each other.
The condition is simple for standing waves: you can only fit an integer number of half wavelenghs on the string.
A wavelength is one complete up-and-down shape.
Thus
L
wavelength = 2 * ---------
n
where n = 1 1st harmonic or fundamental;
2 1st harmonic or 1st overtone;
3 1st harmonic of 2nd overtone;
etc.
and
L is the string length.
wave speed in the string wave speed
frequency = ------------------------- = n -------------
wavelength 2L
The string oscillations set up sounds in the air---which skillfully arranged
are music.
The wave speed can be changed by adjusting the tension in the string.
The string length L can be adjusted by the fingers.
All musical instruments are in many ways like string instruments.
They have their fundamentals and overtones.
The reason musical instruments sound different even when playing at the same fundamental is the varying intensities of the overtones.
It is the distribution of intensities among the harmonics that give a musical instrument its individual voice.
The human vocal folds (vocal cords) (see image) are also a resonater noise-maker whose frequency can be adjusted in ways do know---even if can't explain it.