Learn Physics-vibration and free vibration with damping

Learn Physics-vibration and free vibration with damping

Vibration analysis

Basic vibration analysis can be understood by studying the model simple mass-spring-damper. Complex structures such as the car body can be modelled as "sum" model of mass-spring-damper. This Model is an example of a simple harmonic oscillator

Vibration

Vibration analysis

Free vibration without silencer

In the simplest model of the attenuation is considered negligible, and there is no outside force affecting mass (free vibration).

In these circumstances the prevailing style in the spring the long stretch comparable to Fs x according to Hooke's law, or when it is formulated mathematically:

Fs =-k x

with the k is the spring constant.

According to Newton's second law force posed is proportional to the acceleration of the mass:

Σ F = ma = m {x} = m {d ^ 2 x}: {dt ^ 2} =

Since F = Fs, we get the following ordinary differential equation:

m {x} + k x = 0.

Simple harmonic motion-spring system

If we assume that we start the vibration system with spring-loaded so far A stretch and then release it, the above equations solution describing the mass movements are:

x (t) = A 2cos (2pi. fn. t)

This solution suggests that the mass will oscillate in simple harmonic motion having an amplitude of A frequency and fn fn number is one of the most important quantities in vibration analysis, and called the undamped natural frequency. For a simple mass-spring system, the fn is defined as:

fn = {1: {2pi}}. root {k: m}

Note: the angular frequency ω (ω = 2πf) and units of radians per second is often used in equations because it simplifies the equations, but the magnitude is usually converted into a "standard" frequency (units of Hz) when stating the frequency of the system.

When the mass and stiffness (a k) Note the frequency of vibration of the system will be determined using the formula above.

Vibration

Vibration analysis

Free vibration with damping

When the attenuation is taken into account, means style silencer also applies on a mass in addition to the force caused by stretching the spring. When moving in a fluid object will get attenuation due to the viscosity of the fluid. The style of this viscosity is proportional to the speed of objects. Due to constant viscosity (viscosity) c is a coefficient with units of reducer, N s/m (SI)

The solution to this equation depends on the magnitude of the damping. When damping is small enough, the system will still vibrate, but will eventually stop. This State is called less mute, and is most cases get attention in the analysis of the vibration. When the attenuation is enlarged so that it reaches the point when the system is no longer oscillates we reach a point of critical damping. When the attenuation is added through this critical point of the system referred to in the State through the mute.

To characterize the amount of attenuation in the system used a ratio called the damping ratio. This ratio is the ratio between the actual amount of attenuation attenuation is required to reach the point of critical damping.

Damped natural frequency less than the undamped natural frequency, however, for many practical cases the damping ratio is relatively small, and hence the difference is negligible. Therefore the damped and undamped description is often not mentioned when declaring natural frequency.

Physics waves and wave length

Physics waves and wave length

The waves are vibrations that propagate. The ideal form of a wave motion sinusoide will follow. In addition to electromagnetic radiation and gravitational radiation, which may be able to walk through a vacuum, there are waves on a medium (which because of changes the shape can generate elastic restoring forces) where they can run and can move the energy from one place to another without causing the particles of the medium move permanently; i.e. There is no displacement en masse. In fact, any special point oscillating around one particular position can have an effect on the penis.

A medium called:

linear if different waves at any particular point in the medium can be summed up,

limited if restricted, otherwise it is called unlimited

physical characteristics of uniform if not changed at different points

isotropic in its physical characteristics if the "same" in different directions

The Wavelength

The wavelength is the distance between repeating units of a wave pattern. Usually have denoted the letter lambda (λ) Greece.

In a sine wave, the wavelength is the distance between the peaks.

The x Axis represents length, and I represent the quantity varies (e.g. air pressure for a sound wave or electric or magnetic field strength for light), at a point in the function of time x.

Wavelength λ has an inverse relationship to frequency f, number of peaks to pass a point in a given time. Panjan wave is equal to the speed of the wave divided by the frequency of the wave. When dealing with electromagnetic radiation in a vacuum, this speed is the speed of light c, untuku signal (waves) in the air, it is the speed of sound in air. Connection is::

λ = {c}: {f}

λ = wavelength of a sound wave or electromagnetic waves

c = speed of light in a vacuum = 299, 792.458 km/d ~ 300.000 km/d = 300,000,000 m/s or

c = speed of sound in air = 343 m/s at 20 ° C (68 ° F)

f = the frequency of the wave

Electromagnetic waves

Electromagnetic waves

can be described as two waves of transversal propagated in two perpendicular plane of magnetic field and electric field. Towards magnetic waves will push the electric waves, and vice versa, while climbing, wave power will push the wave magnet. The Diagram above shows a light wave propagating from left to right with the electric field in the vertical plane and horizontal plane on the magnetic field.

light definition physics

light definition physics

At the height of classical optics, light is defined as electromagnetic waves and triggers a series of inventions and ideas, since 1838 by Michael Faraday with the invention of the cathode ray, 1859 with the black mass radiation theory by Gustav Kirchhoff, the 1877 Ludwig Boltzmann said that the status of the physical system energy can be discrete, quantum theory as a model of the theory of the black mass radiation by Max Planck in 1899 with the hypothesis that the energy is absorbed and teradiasi can be divided into discrete sum called energy elements, E. in 1905, Albert Einstein photoelectric effect experiment, making the light that bathes the atom the electrons to excite leapt out of its orbit. On trial in 1924 by Louis de Broglie showed electrons have the nature of duality particle-wave duality theory erupted, up to particle-wave. Albert Einstein later in 1926 make postulates based on photoelectric effect, that light is composed of quanta called photons have the same duality. The works of Albert Einstein and Max Planck received the Nobel Prize respectively in 1921 and 1918 and formed the basis of quantum mechanical theories developed by many scientists, including Werner Heisenberg, Niels Bohr, Erwin Schrödinger, Max Born, John von Neumann, Paul Dirac, Wolfgang Pauli, David Hilbert, Roy j. Glauber and others.

Light 3

This Era came to be called the era of modern optics and light is defined as a transversal electromagnetic-wave dualism and the flow of particles called photons. Further development took place in 1953 with the discovery of x-ray laser and maser, in 1960.

The Era of modern optics, not immediately put an end to the era of classical optics, but introduces the properties of light to another i.e. the diffusion and scattering.

The definition of light

The definition of light

Light is a wave-shaped energy elekromagnetik visible wavelengths approximately 380 – 790 nm. In physics, light is electromagnetic radiation with a wavelength, whether visible or not.

Light is a particle called the photon packet.

Both of the above definition is shown simultaneously so that the light is called the "wave-particle duality". Packets of light called the spectrum then are perceived visually by the sense of sight as the color. The study of light, known as optics, is an important research area in modern physics.

Study of light began with the advent of the era of classical optics, the study of optical quantities such as: intensity, frequency or wavelength, polarization and phases of light. The properties and interactions of light around a geometric approach to partially done such as reflection and refraction, optical properties of fisisnya and approach are: interference, diffraction, dispersion, polarization. Each study of classical optics, this is called geometrical Optics (en: geometrical optics) and physical Optics (en: physical optics).